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### Stata FAQ: How can I see the number of missing values and patterns of missing values in my data file?

Sometimes, a data set may have "holes" in it, that is, missing values. Some statistical procedures such as regression analysis will not work as well, or at all, on a data set with missing values.  The observations with missing values have to be deleted or the missing values have to be substituted in order for a statistical procedure to produce meaningful results. Most statistical programs (including SAS, SPSS, and Stata) will automatically remove such cases from any analysis you run (without deleting the cases from the dataset). This is why the "n" often varies from analysis to analysis, even if the dataset is the same. Different variables have different amounts of missing data and hence, changing the variables in a model changes the number of cases with complete data on all the variables in the model. Because the software drops cases with missing values for us, it is very easy to "forget" about missing data entirely. However, the presence of missing data can influence our results, especially when a dataset or even a single variable, has a high percentage of values missing. Thus it is always a good idea to check a dataset for missing data, and to think about how the missing data may influence our analyses. This page shows a few methods of looking at missing values in a dataset, this information can be used to make better informed decisions about how to handle the missing values.

Before we begin, we need some data with missing values, the code below inputs a small dataset into Stata, and then displays that data. In a small dataset, like the one below, it is very easy to look at the raw data and see where values are missing. However, when datasets are large, we need a more systematic way to examine our dataset for missing values. Below we show you some ways to do that, using the data below as an example.

clear
input landval  improval    totval  salepric saltoapr
30000     64831     94831    118500   1.25
30000     50765     80765     93900    .
46651     18573     65224         .   1.16
45990     91402         .    184000   1.34
42394         .     40575    168000   1.43
.      3351     51102    169000   1.12
63596      2182     65778         .   1.26
56658     53806     10464    255000   1.21
51428     72451         .         .   1.18
93200         .      4321    422000   1.04
76125     78172     54297    290000   1.14
.     61934     16294    237000   1.10
65376     34458         .    286500   1.43
42400         .     57446         .    .
40800     92606     33406    168000   1.26
end

list

+---------------------------------------------------+
| landval   improval   totval   salepric   saltoapr |
|---------------------------------------------------|
1. |   30000      64831    94831     118500       1.25 |
2. |   30000      50765    80765      93900          . |
3. |   46651      18573    65224          .       1.16 |
4. |   45990      91402        .     184000       1.34 |
5. |   42394          .    40575     168000       1.43 |
|---------------------------------------------------|
6. |       .       3351    51102     169000       1.12 |
7. |   63596       2182    65778          .       1.26 |
8. |   56658      53806    10464     255000       1.21 |
9. |   51428      72451        .          .       1.18 |
10. |   93200          .     4321     422000       1.04 |
|---------------------------------------------------|
11. |   76125      78172    54297     290000       1.14 |
12. |       .      61934    16294     237000        1.1 |
13. |   65376      34458        .     286500       1.43 |
14. |   42400          .    57446          .          . |
15. |   40800      92606    33406     168000       1.26 |
+---------------------------------------------------+

#### 1. Number of missing values vs. number of  non missing values

The first thing we are going to do is determine which variables have a lot of missing values. We have created a small Stata program called mdesc that counts the number of missing values in both numeric and character variables. You can download mdesc from within Stata by typing findit mdesc (see How can I use the findit command to search for programs and get additional help? for more information about using finidit).

Then you can run mdesc for one or more variables as illustrated below.

mdesc

Variable      Missing      Total     Missing/Total
------------------------------------------------------------
landval           2          15        .133333
improval           3          15             .2
totval           3          15             .2
salepric           4          15        .266667
saltoapr           2          15        .133333
Now we know the number of missing values in each variable. For instance, variable salepric has four missing values and saltoapr has two missing values.

#### 2. Obtaining the number of missing values per observation

We can also look at the distribution of missing values across observations. The code below creates a variable called nmis that gives the number of missing values for each observation. The function rmiss2() used here is an extension to the egen function rmiss(). It counts the number of missing values in the varlist. rmiss2() accepts both string and numeric variables. (Stata's rmiss() only accepts numeric variables.) You can download rmiss2() over the internet from within Stata by typing findit rmiss2 (see How can I use the findit command to search for programs and get additional help? for more information about using findit).

egen nmis=rmiss2(landval improval totval salepric saltoapr)

Below we tabulate the variable we just created. Looking at the frequency table we know that there are four observations with no missing values, nine observations with one missing values, one observation with two missing values and one observation with three missing values.

tab nmis

nmis |      Freq.     Percent        Cum.
------------+-----------------------------------
0 |          4       26.67       26.67
1 |          9       60.00       86.67
2 |          1        6.67       93.33
3 |          1        6.67      100.00
------------+-----------------------------------
Total |         15      100.00

#### 3. Patterns of missing values

We can also look at the patterns of missing values. You can download mvpatterns over the internet from within Stata by typing findit mvpatterns (see How can I use the findit command to search for programs and get additional help? for more information about using findit). The command mvpatterns produces output for all variables in the dataset, for missing data patterns across a subset of variables, a variable list can be included, for example, mvpatterns landval improval totval.

The output produced by mvpatterns is shown below. The first table lists the variables, their storage type (type), the number of observations (obs), the number of missing values (mv), and the variable label if the variables has one. The second table contains the information on the pattern of missing values. The first block of columns in the output shows the patterns of missing data. Within the block, each variable is represented by a column, a "+" indicates that values of that variable are present in a given missing data pattern, a "." indicates that they are missing. The columns follow the same order as the variable list in the first table, so that the first column in the output below represents landval, the second improval, and so on. The missing data patterns are listed in descending frequency, here the most common missing data pattern is complete data ("+++++"). The table also shows the number of missing values in that pattern (_mv), and the number of cases with that missing data pattern (_freq). Based on the information in the second table we know that there are four observations with no missing values, two cases missing on just the variable salepric, and one observation with missing values on improval, salepric and saltoapr.

mvpatterns

Variable     | type     obs   mv   variable label
-------------+-----------------------------------
landval      | float     13    2
improval     | float     12    3
totval       | float     12    3
salepric     | float     11    4
saltoapr     | float     13    2
-------------------------------------------------

Patterns of missing values

+------------------------+
| _pattern   _mv   _freq |
|------------------------|
|    +++++     0       4 |
|    +++.+     1       2 |
|    ++.++     1       2 |
|    +.+++     1       2 |
|    .++++     1       2 |
|------------------------|
|    ++++.     1       1 |
|    ++..+     2       1 |
|    +.+..     3       1 |
+------------------------+

#### 4. When all the variables of interest are numeric

The examples above all work regardless of whether the variables of interest (i.e. the variables whose missing data patterns you want to examine) are numeric or string. When all of the variables you wish to check for missing values are numeric we can use a program called misschk to simplify the steps of examining the missing data in our dataset. (Note: numeric variables include those with value labels that are strings, as long as the actual values of the variables are stored as numbers.) You can download misschk from within Stata by typing findit misschk (see How can I use the findit command to search for programs and get additional help? for more information about using findit).

Below is the command for misschk. We have listed all five of the variables in our dataset in the variable list after the misschk command. However, we could have just left the list of variables blank (i.e. used only misschk , gen(miss) instead), if we had, misschk would have run using all the variables in our dataset. The variable list is only necessary if we want to run misschk on only some of the variables in our dataset. The gen(miss) option tells misschk that we want it to create two new variables, both of which start with "miss". These two variables will be named misspattern and missnumber. The variable misspattern indicates which of the missing data patterns each case follows. The variable missnumber indicates the number of missing values for each case.

misschk landval improval totval salepric saltoapr, gen(miss)

The output for misschk consists of three tables. The first table lists the number of missing values, as well as percent missing for each variable, this is similar to the table produced by mdesc in part 1 above. This table also contains a column labeled "#" which assigns each variable a number that is used to identify the variable later on in the output. The second table shows the distribution of missing values. The pattern of missingness is described using the variable numbers from the first table, and underscores ("_"). The numbers indicate which variables are missing in that pattern, the underscores represent non-missing observations. For example, from the second table we see that two cases have missing values on variable 1 (landval), but complete data on all other variables, and that one case is missing data on variables 2, 4, and 5. The bottom row shows that four cases are not missing any values at all (all underscores). This table shows the same information generated in part three above, but in a slightly different format. The missing data pattern for each case is described in the variable misspattern. Finally, the third table shows the distribution of the number of missing values per case. This is the same information discussed above in part 2. The number of variables each case is missing is also contained in the variable missnumber.

Variables examined for missing values

#  Variable        # Missing   % Missing
--------------------------------------------
1  landval               2        13.3
2  improval              3        20.0
3  totval                3        20.0
4  salepric              4        26.7
5  saltoapr              2        13.3

Missing for |
which |
variables? |      Freq.     Percent        Cum.
------------+-----------------------------------
1____ |          2       13.33       13.33
_2_45 |          1        6.67       20.00
_2___ |          2       13.33       33.33
__34_ |          1        6.67       40.00
__3__ |          2       13.33       53.33
___4_ |          2       13.33       66.67
____5 |          1        6.67       73.33
_____ |          4       26.67      100.00
------------+-----------------------------------
Total |         15      100.00

Missing for |
how many |
variables? |      Freq.     Percent        Cum.
------------+-----------------------------------
0 |          4       26.67       26.67
1 |          9       60.00       86.67
2 |          1        6.67       93.33
3 |          1        6.67      100.00
------------+-----------------------------------
Total |         15      100.00

The content of this web site should not be construed as an endorsement of any particular web site, book, or software product by the University of California.


text:
# Margin of error

34,203pages on
this wiki

The margin of error is a statistic expressing the amount of random sampling error in a survey's results. The larger the margin of error, the less confidence one should have that the poll's reported results are close to the "true" figures; that is, the figures for the whole population.

The margin of error is usually defined as the radius of the confidence interval for a particular statistic from a survey. When a single, global margin of error is reported for a survey, it refers to the maximum margin of error for all reported percentages using the full sample from the survey. This maximum margin of error can be calculated as the radius of the confidence interval for a reported percentage of 50%.

Like confidence intervals, the margin of error can be defined for any desired confidence level, but usually a level of 90%, 95% or 99% is chosen (typically 95%). This level is the probability that a margin of error around the reported percentage would include the "true" percentage. Along with the confidence level, the sample design for a survey, and in particular its sample size, determines the magnitude of the margin of error. A larger sample size produces a smaller margin of error, all else remaining equal.

The margin of error only takes random sampling error into account. It does not represent other potential sources of error or bias such as poorly phrased questions, people lying or refusing to respond, the exclusion of people who could not be contacted, or miscounts and miscalculations.

## ConceptEdit

### Running exampleEdit

A running example from the 2004 U.S. presidential campaign will be used to illustrate concepts throughout this article. According to an October 2, 2004 survey by Newsweek, 47% of registered voters would vote for John Kerry/John Edwards if the election were held on that day, 45% would vote for George W. Bush/Dick Cheney, and 2% would vote for Ralph Nader/Peter Camejo. The size of the sample was 1,013.[1] Unless otherwise stated, the remainder of this article uses a 95% level of confidence.

### Basic conceptEdit

Polls typically involve taking a sample from a certain population. In the case of the Newsweek poll, the population of interest is the population of people who will vote. Because it is impractical to poll everyone who will vote, pollsters take smaller samples that are intended to be representative; that is, a random sample of the population.[2] It is possible that pollsters sample 1,013 voters who happen to vote for Bush when in fact the population is split, but this is extremely unlikely given that the sample is random.

Sampling theory provides methods for calculating the probability that the poll results differ from reality by more than a certain amount, simply due to chance; for instance, that the poll reports 47% for Kerry but his support is actually as high as 50%, or is really less than 44%. This theory and some Bayesian assumptions suggest that the "true" percentage will probably be fairly close to 47%. The more people that are sampled, the more confident pollsters can be that the "true" percentage is close to the observed percentage. The margin of error is a measure of how close the results are likely to be.

However, the margin of error only accounts for random sampling error, so it is blind to systematic errors that may be introduced by non-response or by interactions between the survey and subjects' memory, motivation, communication and knowledge.[3]

### Calculations assuming random samplingEdit

This section will briefly discuss the standard error of a percentage, the corresponding confidence interval, and connect these two concepts to the margin of error. For simplicity, the calculations here assume the poll was based on a simple random sample from a large population.

The standard error of a reported proportion or percentage p measures its accuracy, and is the estimated standard deviation of that percentage. It can be estimated from just p and the sample size, n, if n is small relative to the population size, using the following formula:[4]

Standard error = $\sqrt{\frac{p(1-p)}{n}}$

When the sample is not a simple random sample from a large population, the standard error must be estimated through more advanced calculations.

In the Newsweek poll, Kerry's level of support p = 0.47 and n = 1,013. The standard error (.016 or 1.6%) helps to give a sense of the accuracy of Kerry's estimated percentage (47%). A Bayesian interpretation of the standard error is that although we do not know the "true" percentage, it is highly likely to be located within two standard errors of the estimated percentage (47%). The standard error can be used to create a confidence interval within which the "true" percentage should be to a certain level of confidence.

The estimated percentage plus or minus its margin of error is a confidence interval for the percentage. In other words, the margin of error is half the width of the confidence interval. It can be calculated as a multiple of the standard error, with the factor depending of the level of confidence desired; a margin of one standard error gives a 68% confidence interval, while the estimate plus or minus 1.96 standard errors is a 95% confidence interval, and a 99% confidence interval runs 2.58 standard errors on either side of the estimate.

### DefinitionEdit

The margin of error for a particular statistic of interest is usually defined as the radius (or half the width) of the confidence interval for that statistic.[5][6] The term can also be used to mean sampling error in general. In media reports of poll results, the term usually refers to the maximum margin of error for any percentage from that poll.

### Maximum margin of errorEdit

The maximum margin of error for any percentage is the radius of the confidence interval when p = 50%. As such, it can be calculated directly from the number of poll respondents. For 95% confidence, assuming a simple random sample from a large population:

(Maximum) margin of error (95%) = 1.96 × $\sqrt{\frac{0.5(1-0.5)}{n}} = \frac{0.98}{\sqrt{n}}$

This calculation gives a margin of error of 3% for the Newsweek poll, which reported a margin of error of 4%. The difference was probably due to weighting or complex features of the sampling design that required alternative calculations for the standard error.

### Different confidence levelsEdit

For a simple random sample from a large population, the maximum margin of error is a simple re-expression of the sample size n. The numerators of these equations are rounded to two decimal places.

Margin of error at 99% confidence $\approx 1.29/\sqrt{n}\,$
Margin of error at 95% confidence $\approx 0.98/\sqrt{n}\,$
Margin of error at 90% confidence $\approx 0.82/\sqrt{n}\,$

If an article about a poll does not report the margin of error, but does state that a simple random sample of a certain size was used, the margin of error can be calculated for a desired degree of confidence using one of the above formulae. Also, if the 95% margin of error is given, one can find the 99% margin of error by increasing the reported margin of error by about 30%.

### Maximum and specific margins of errorEdit

While the margin of error typically reported in the media is a poll-wide figure that reflects the maximum sampling variation of any percentage based on all respondents from that poll, the term margin of error also refers to the radius of the confidence interval for a particular statistic.

The margin of error for a particular individual percentage will usually be smaller than the maximum margin of error quoted for the survey. This maximum only applies when the observed percentage is 50%, and the margin of error shrinks as the percentage approaches the extremes of 0% or 100%.

In other words, the maximum margin of error is the radius of a 95% confidence interval for a reported percentage of 50%. If p moves away from 50%, the confidence interval for p will be shorter. Thus, the maximum margin of error represents an upper bound to the uncertainty; one is at least 95% certain that the "true" percentage is within the maximum margin of error of a reported percentage for any reported percentage.

### Effect of population sizeEdit

The formulae above for the margin of error assume that there is an infinitely large population and thus do not depend on the size of the population of interest. According to sampling theory, this assumption is reasonable when the sampling fraction is small. The margin of error for a particular sampling method is essentially the same regardless of whether the population of interest is the size of a school, city, state, or country, as long as the sampling fraction is less than 10%.

### Other statisticsEdit

Confidence intervals can be calculated, and so can margins of error, for a range of statistics including individual percentages, differences between percentages, averages, medians[7] and totals.

The margin of error for the difference between two percentages is larger than the margins of error for each of these percentages, and may even be larger than the maximum margin of error for any individual percentage from the survey.

## Comparing percentagesEdit

In a plurality voting system, it is important to know who is ahead. The terms "statistical tie" and "statistical dead heat" are sometimes used to describe reported percentages that differ by less than a margin of error, but these terms can be misleading.[8][9] For one thing, the margin of error as generally calculated is applicable to an individual percentage and not the difference between percentages, so the difference between two percentage estimates may not be statistically significant even when they differ by more than the reported margin of error. The survey results also often provide strong information even when there is not a statistically significant difference.

When comparing percentages, it can accordingly be useful to consider the probability that one percentage is higher than another.[10] In simple situations, this probability can be derived with 1) the standard error calculation introduced earlier, 2) the formula for the variance of the difference of two random variables, and 3) an assumption that if anyone does not choose Kerry they will choose Bush, and vice versa; they are perfectly negatively correlated. This may not be a tenable assumption when there are more than two possible poll responses. For more complex survey designs, different formulas for calculating the standard error of difference must be used.

The standard error of the difference of percentages p for Kerry and q for Bush, assuming that they are perfectly negatively correlated, follows:

Standard error of difference = $\sqrt{\frac{p(1-p)+q(1-q)+2pq}{n}}.$

Given the observed percentage difference pq (2% or 0.02) and the standard error of the difference calculated above (.03), any statistical calculator may be used to calculate the probability that a sample from a normal distribution with mean 0.02 and standard deviation 0.03 is greater than 0.

Applying these calculations to the Newsweek example results in a 75% probability that Kerry was "truly" leading.

## NotesEdit

1. Newsweek (2004-10-02). NEWSWEEK POLL: First Presidential Debate. Press release. Retrieved on 2006-05-31.
2. Wonnacott and Wonnacott (1990), pp. 4–8.
3. Sudman, S.L. and Bradburn N.M. (1982) Asking Questions. Jossey-Bass: pp. 17-19
4. Sample Sizes, Margin of Error, Quantitative Analysis
5. Lohr, Sharon L. (1999). Sampling: Design and Analysis, 49, Pacific Grove, California: Duxbury Press. "The margin of error of an estimate is the half-width of the confidence interval ..."
6. Stokes, Lynne, Tom Belin (2004). What is a Margin of Error?. (PDF) What is a Survey?. Survey Research Methods Section, American Statistical Association. URL accessed on 2006-05-31.
7. Income - Median Family Income in the Past 12 Months by Family Size, U.S. Census Bureau. Retrieved February 15, 2007.
8. Braiker, Brian. "The Race is On: With voters widely viewing Kerry as the debate’s winner, Bush’s lead in the NEWSWEEK poll has evaporated". MSNBC, October 2, 2004. Retrieved on 2007-02-02.
9. Rogosa, D.R. (2005). A school accountability case study: California API awards and the Orange County Register margin of error folly. In R.P. Phelps (Ed.), Defending standardized testing (pp. 205–226). Mahwah, NJ: Lawrence Erlbaum Associates.
10. Drum, Kevin. Political Animal, Washington Monthly, August 19, 2004. Retrieved on 2007-02-15.

## ReferencesEdit

• Sudman, Seymour and Bradburn, Norman (1982). Asking Questions: A Practical Guide to Questionnaire Design. San Francisco: Jossey Bass. ISBN 0875895468
• Wonnacott, T.H. and R.J. Wonnacott (1990). Introductory Statistics, 5th ed., Wiley. ISBN 0471615188.

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We practice more computations and think about what integrals mean.

In this section we will continue to set-up (and sometimes compute) double and triple integrals and think about what these mean.

### Triangles

It’s important to do a self-check to see if our purported value for an integral is at all plausible.

The region $$ is a triangle with base $$ and height $$, so the area of the region $$ is $$ which is about $$ square units. In other words, which also means that We are claiming that $$ equals $$, which is about $$.

When $$, the value of $$ is sometimes positive, sometimes negative, but at least we know that and this inequality then implies that So $$ is certainly in the ballpark of plausibility.

### Polar coordinates

Again consider the region How does compare to
$$ $$ $ B ]]>$

### Spheres and hemispheres

Again let $$ be the region Set $$ and $$. How does $$ relate to $$?
$$ $$ $ B ]]>$


text:
loft

comments in german, french and russian will be translated into english.
you can use LaTeX in your math comments, by using the $shortcode: [latex] E = m c^2$


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# Generalized Parity Games

We consider games where the winning conditions are disjunctions (or dually, conjunctions) of parity conditions; we call them \emph{generalized} parity games. These winning conditions, while $\omega$-regular, arise naturally when considering fair simulation between parity automata, secure equilibria for parity conditions, and determinization of Rabin automata. We show that these games retain the computational complexity of Rabin and Streett conditions; i.e., they are NP-complete and co-NP-complete, respectively. The (co-)NP-hardness is proved for the special case of a conjunction/disjunction of two parity conditions, which is the case that arises in fair simulation and secure equilibria. However, considering these games as Rabin or Streett games is not optimal. We give an exposition of Zielonka's algorithm when specialized to this kind of games. The complexity of solving these games for $k$ parity objectives with $d$ priorities, $n$ states, and $m$ edges is $O(n^{2 k d} \cdot m) \cdot \frac{(k\cdot d)!}{d!^k}$, as compared to $O(n^{2 k d} \cdot m) \cdot (k\cdot d)!$ when these games are solved as Rabin/Streett games. We also extend the subexponential algorithm for solving parity games recently introduced by Jurdzi{\'n}ski, Paterson, and Zwick to generalized parity games. The resulting complexity of solving generalized parity games is $n^{O(\sqrt{n})} \cdot \frac{(k\cdot d)!}{d!^k}$. As a corollary we obtain an improved algorithm for Rabin and Streett games with $d$ pairs, with time complexity $n^{O(\sqrt{n})} \cdot d!$.

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CAPM goodness of fit

I want to test the CAPM. I have collected monthly data from 1-9-2012 to 1-9-2017. I have data from the return of Standard&Poor's 500 and data from various US companies. The beta's seem right, but my goodness of fit ($R^2$) are low: Ameren 0.0614, Apple 0.2456. My question is: Can this be right? If you're testing the CAPM or am I doing something wrong. I used the CAPM regression $R_{i,t}-R_{f,t}=\alpha_i+\beta_i(R_{M,t}-R_{f,t})+e_i$.

• What estimation procedure are you using? Are you running regressions in two stages: one to find the betas and the other to test the CAPM? If this is the case, which regression are you talking about when you talk about the $R^2$ ? – jmbejara Sep 26 '17 at 2:19
• I am using OLS. I just one regression: the regression descriped above for 20 stocks. Fama-Macbeth had in their 1973 paper beautifull R^2's, so I was wondering if I did something wrong. But my question was answered splendidly by a number of people below. My thanks! – Cardinal Sep 27 '17 at 13:22
• OK. Sounds good. But just to clarify, the Fama-Macbeth procedure uses two regressions. The first is a time series regression to obtain the betas. The second is a cross-sectional regression to regress the risk-premia of each security on their betas. The CAPM hypothesis puts restrictions on the second regression, not the first. So, since your question is about interpreting the first regression, your question doesn't really have anything to do with testing the CAPM. This confusion is why I claimed that the question was probably a little ambiguous. – jmbejara Sep 27 '17 at 22:02

$\beta$ is the measure of the sensitivity of stock returns to market returns. This has nothing to do with the value of $R^2$.
Your results appear to be fine, you can get significant beta estimates but low $R^2$. Why?
As measured by $R^2$, 24.56% of variation in Apple returns is accounted for by the variation in the market index, $S$&$P 500$. Clearly, there must be other factors that determine the remaining 75.44$% of variation in the Apple returns. Other factors that you could include in the model are copmany size and market to book value (Fama and French Three-Factor Model). By including these omitted variables in your new model, you may achieve higher r-squared value. First note the variables$\alpha_i$and$e_i$are completely degenerated, there's no way to tell one apart from the other, unless you have a strong prior on them. The model should look something like $$R_i = R_f + \beta (R_{m,i} - R_f) + e_i \tag{1}$$ which can be rewritten in the form $$R_i = \beta_0 + \beta R_{m,i} + e_i \tag{2}$$ For the example below I selected Apple as my asset (with returns labeled rasset) and S&P 500 as the market index (with returns labeled rmarket), this for the window 2012-09-01 to 2017-09-01. This is a summary of OLR applied to Eq (2) You're right, the correlation between the two is low, which you can actually already see from a plot of the returns However, you can see from the table above that $$P(>|t|) = 0$$ for the coefficient$\beta$, which means you're almost 100\% sure that$\beta\not = 0$• This question doesn't (at least directly) address the OP's concern over the$R^2$. – jmbejara Sep 26 '17 at 19:54 Note: I'm adding this simply to supplement the other answers. Also, I'm going to assume that you're talking about the$R^2$of the time series regression of security$i$on the market portfolio$M$$$R_{it} = \alpha_i + \beta_i R_{Mt} + \epsilon_{it}.$$ As @london described in his answer, the$\beta_i$is simply the sensitivity of security$i$to the market. In the Sharpe-Lintner CAPM, as well as in other variations, systematic risk is then defined as$\beta^2 \cdot \sigma^2_{R_M}$and idiosyncratic risk is$\sigma^2_{\epsilon_i}$. Thus, the$R^2$(r-squared) of this regression should not be interpreted so much as "goodness of fit." Rather, it is simply a measure of the ratio of ratio of systematic risk to total risk (systematic plus idiosyncratic risk). As @london described, total risk includes all the other things that drive security$i$'s returns. To see this, note that the definition of$R^2\$ in the population sense is $$R^2 = \frac{\beta_i^2 \sigma^2_{M}}{\beta_i^2 \sigma^2_M + \sigma_\epsilon^2}.$$


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# SmoothDyn

## Problem 155

(Thurston-Sullivan?) Are all smooth actions of $\Phi _g$ on $\mathbb S^1$ which are topologically conjugate to a standard one differentiably conjugate to the standard one?

## Problem 150

Is there an expansive homeo of $\mathbb S^2$?

## Problem 142

Can the  adding machine be an invariant set for a $C^2$ mapping of the 2-disk? of the $n$-disk?

## Problem 138

Billiards in right angle triangles. Find examples when it is ergodic.

## Problem 136

For most $C^2$ maps $f : [0,1] \to [0,1]$, for all $\epsilon >0$ there is a hyperbolic set $\Lambda$ such that $h(f|\Lambda) \geq h(f) - \epsilon.$ (See question 8c.)

## Problem 133

$C^ \infty$ diffeo of the 2-disk preserving a smooth measure $\mu$ with $h_\mu >0$? An ergodic example?

## Problem 132

$\dot X = Q(X)$ on $\mathbb{R}^3$, where $Q$ is quadratic. Is there a condition on the coefficients which guarantees a homoclinic point (a complicated attractor)? E.g. like for Reynolds numbers?

## Problem 131

$h(f)$ given by periodic points for generic $C^1$ map from $I$ to $I$? (or generic continuous map?)

## Problem 122

Fibration Theorem for $\log |\lambda|$? If $M = \cup _\alpha N_\alpha, N_\alpha$ submanifolds, with $f(N_\alpha ) = N_\alpha$, is the spectral radius of $f_\ast$ on $M$ $\le$ the sup of the spectral radius of $f_\ast$ on $N_\alpha$'s?

If $f|N_\alpha$ is an isometry, does the spectral radius of $f_\ast$ on $M$ $= 1$? Are all distal diffeos built up this way, i.e. by extensions where homology works?

Note: There is another Problem 122 that was crossed out.

## Problem 120

Entropy 0 for differentiable action of $G = \mathbb{R}^n$ or $\mathbb{Z}^n (n \geq 2).$ For nilpotent $G$. General Lie group $G$?

## Problem 119

(Thom) $Grad F$ for real analytic $F:\mathbb{R}^n \to \mathbb{R}$. Stratification of orbits near a singular point.

## Problem 117

(Sullivan) Show that $|\lambda| = 1$ for $f: M \to M$, where $f$ is  $C^1$ and distal and $\lambda$ is an eigenvalue of $f_\ast$. Is $f \sim g$ for some Morse Smale $g$?

## Problem 115

Are analytic maps $h$-expansive?

## Problem 113

For a rational function $f(z)$ giving a degree $n$ map $z \mapsto f(z)$ of $\mathbb S^2$, does this map have entropy $\log n?$

($\ge$ by Misurewicz and = a.e. by Guckenheimer)

## Problem 104

Note: $\frac {1}{1-t} \; = \; \Pi _{n= 0}^\infty (1 +t^{2^n})$ in $Z[[ t]]$. Is there a $C^2$ map $\mathbb D^2 \to \mathbb D^2$ so that.....

## Problem 103

How can you write $1 +t +t^2 \; = \; \Pi _{i=0 }^\infty (1\pm t^{n_i})$ in $Z[[ t]] ?$

## Problem 102

Is the false zeta function of a basic set ....? Define false zeta function for a flow basic set

## Problem 100

This problem isn't clearly legible, but it is thought to say: Symbolic dynamics for Abraham-Smale, Newhouse, Lorentz

## Problem 96

KAM Theorem using $\mu$ uniquely ergodic  flows on $M$ without assuming $M = T^n$

## Problem 94

Does every manifold $M^n, n\geq 3$ admit a smooth Bernoulli flow (Ruelle)?

## Problem 91

Is the topological entropy continuous on $C^1$ expanding maps of the interval? (a.e. continuous?)

## Problem 88

Index 0 fixed point of diffeo is removable by small perturbation (Hirsch)

## Problem 80

Reddy examples of expansive maps. Related to Anosov diffeos. Are expansive diffeos likely to be Anosov?

## Problem 76

Does $h(f)$ have a minimum in isotopy class?

## Problem 69

Is $h: Diff ^r \to \mathbb{R}$ generically continuous for some $r$?

## Problem 66

Central Limit Theorem, other strong statistics near an attractor of a diffeo.

## Problem 64

Entropy of group actions. There is no smooth $\mathbb{R}^n$- (or $\mathbb{Z}^n$-) action with positive entropy when $n >1$. Is this true for all Lie groups (or lattices) of dimension greater than 1? Try $N$ nilpotent.

## Problem 63

$C^r$ diffeos that are not $C^{r+1}$ qualitatively. Find a $C^1$ diffeo $f : V \to V$ and a $C^1$ embedding $g:V \to M$ and $\tilde f$ extending $f$ to $M$ such that $\tilde f$ is $C^2$ on $M$, but $\tilde f |V$ is qualitatively not $C^2$ (i.e. the qualitative behavior of $\tilde f|V$ is due to the irregularity of $V$ but not of $\tilde f$)

## Problem 60

Study flows $H = V(r) + \frac{1}{2} mv^2$ for various (?) continuous $V(r)$. Statistical mechanics literature (Hénon -?, Toda,...)

## Problem 50

Is there a transitive/ergodic diffeomophism on $\mathbb S^2, \mathbb D^2$?

## Problem 49

Does minimal or uniquely ergodic for a diffeo  $f$ implies $h(f) = 0$ (try homeo case too)?

1. Is there a minimal diffeo homotopic to $\left( \begin{matrix} 2 & 1\\ 1& 1 \end{matrix} \right) \times Id.$ on $\mathbb T^3$?
2. (Seifert conjecture) Minimal flow on $\mathbb S^3$.

## Problem 48

Suppose $F: C \to \mathbb{R}, C$ the Cantor set, has bounded total variation. Is there a homeo $g : [0,1] \to [0,1]$ and a diffeo (Lipschitz, maybe) $f:[0,1] \to \mathbb{R}$ such that $F = f\circ g |C.$

## Problem 47

Any entropy-like invariant for singularity of diff. maps?

## Problem 42

Is $h(\varphi_t | E)$ differentiable in $E$ for Hamiltonian flows? Any relation to classical or quantum statistical mechanics?

## Problem 27

Construction of a 2-dimensional Hamiltonian diffeo. with an ergodic set of positive measure.

## Problem 16

Brownian motion or diffusion given a flow

## Problem 14

Suspensions of diffeos. -  Are they generically not  (conjugated to) constant time suspensions? what is the strongest statement for Axiom A attractors?

## Problem 10

Statistics plus dynamics of transformations of $[0,1]$ - 'non-linear' $\beta$-expansions like examples.


text:
Public Group

# Having some issues with fstream

This topic is 4683 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

For some reason, once the stream gets to the EOF, it stops working properly. I can't move anywhere else in the stream, I can't write naything to it, or read anything from it. Anything I attempt to read is spimply blank, anything I try to write never gets written, and when ever I try to move back to the begining it doesn't budge =/ here's a little test program:
/*The program*/
#include <fstream>
#include <string>

int main ()
{
string s;
string t;
fstream File("myfile.txt", ios::in | ios::out);

while(File >> s) cout << s << endl;
File.seekp(ios::beg);
File >> t;
File.seekp(ios::end);
File << t;

}

myfile.txt ------------------
abc 123 look at me!

the output is:
abc
123
look
at
me!
<return>

and myfile.txt ends up looking like this: ------------------
abc 123 look at me!

=/ if anyone has any ideas, big thanks^^ Meow.

##### Share on other sites
I think you want seekg and not seekp.

EDIT:
Quote:
 Original post by KuroKittenMeow.

[attention]

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When your stream hits the EOF, try using clear() to reset the status bits on the stream.

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well, i tried using seekg() and that didn't end up any different. i'm not sure where i should use clear()... i tried it in some places, and again, no difference...

lol, yeah, i always try to end posts with a meow of some sort, adds flavor XD

Mrow!

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Okay, I tested it out myself, so this should work:

/*The program*/#include <fstream>#include <string>int main (){	string s;	string t;	fstream File("myfile.txt", ios::in | ios::out);		while(File >> s) cout << s << endl;	File.clear();	File.seekg(0, ios::beg);	File >> t;	File.seekp(0, ios::end);	File << t;}

I think what this means is that once you reach EOF for a stream it gets into a bad state so you have to clear it first, then seek back to the beginning.

EDIT2: Okay, fixed. I don't know why File.seekp(0, ios::end) works but File.seekp(ios::end) doesn't. Anyone know why?

EDIT3: According to a nice book I have once you reach EOF an EOF bit is set for the status flag, so that's why the file needs to be cleared before doing anything else, since it's considered an error flag (the stream isn't considered good anymore). Also, the ios::beg/ios::end/ios::cur flags are meant for relative positions, which is why it has to be File.seekp(0, ios::end) instead of File.seekp(ios::end). Also, that means it should be File.seekg(0, ios::beg) too. I don't know why File.seekg(ios::beg) seemed to work though. Anyone know why?

[Edited by - load_bitmap_file on December 18, 2005 10:16:14 PM]

##### Share on other sites
I'm still getting weird stuff with that... It seems to move around better now, but it still wont right to the file... if i open the file with an additional ios::app command it appends fine, but always returns down before doing so, and doesn't seem to read fromt he file right =/

Mreow.

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Quote:
 Original post by KuroKittenI'm still getting weird stuff with that... It seems to move around better now, but it still wont right to the file... if i open the file with an additional ios::app command it appends fine, but always returns down before doing so, and doesn't seem to read fromt he file right =/Mreow.

Sorry, I posted prematurely [embarrass]. My previous post has the program correct now.

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Hmm, well it seems to run smoother, however it's not printing anything ont he end of the file... the file remains unchanged =/

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Quote:
 Original post by load_bitmap_fileAlso, that means it should be File.seekg(0, ios::beg) too. I don't know why File.seekg(ios::beg) seemed to work though. Anyone know why?

My guess would be that ios::beg is enumerated as 0, ios::cur is 1, and ios::end is 2. So if you pass ios::beg in as a position, it would behave ok. ios::end or ios::cur will not. Another reason C++ is evil [evil].

-edit- But your code that you have now works for me.

[Edited by - nprz on December 18, 2005 11:09:19 PM]

##### Share on other sites
pass in ios::end-1 and that should put the ptr right before the eof

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angular momentum of electron in 3p orbital

The angular momentum of an electron in 4s orbital, 3p orbitals ajnd 4th orbit are . Try it now. This indicates the ratio of Cl-37 and Cl-35 is approximately. Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity (in radians/sec) about a particular axis. Related questions 1) The orbital angular momentum of an electron in 2s orbital is: (IIT JEE-1996) a) 0.5h/π . CBSE has reduced the syllabus for class 10 & 12 exam 2021, date sheet can release soon. Due to the spin-orbit interaction in the atom, the orbital angular momentum no longer commutes with the Hamiltonian, nor does the spin. JEE Main 2021 January session likely to be postponed to February. For the electrons of oxygen atom, which of the following statements is correct? MP Board Exam 2021 - MPBSE Reduces Class 10, 12 Syllabus by 30 Percent. Question From class 11 Chapter STRUCTURE OF ATOM. 1 answer. (ii) The mass of electron is equal to the mass of neutron. Match the following species with their corresponding ground state electronic configuration. (iv) Characteristics of cathode rays depend upon the nature of gas present in the cathode ray tube. NEET 2020 Admissions - MBBS seats reserved for child of COVID-19 warriors who lost their lives due to COVID-19 or died accidentally during COVID-19 duty. CBSE board exam 2021 preparation tips to ace the exam. In which orbital may ti be present ? ℓ = 0, "p" type sublevels have ℓ = 1, "d" type sublevels have ℓ = 2, and "f" type sublevels have ℓ = 3. (i) They start from the cathode and move towards the anode. Hydrogen atom has only one electron, so mutual repulsion between electrons is absent. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. The azimuthal quantum number ℓ describes the orbital angular momentum of each electron and is a non-negative integer. There are two descriptions for the coupling of angular momentum. NEET 2020 - 5 MBBS Seats Reserved for Wards of COVID-19 Warriors. the number of spin states equals 2 corresponding to $$\alpha$$ and $$\beta$$. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula. Chlorine exists in two isotopic forms, Cl-37 and Cl-35 but its atomic mass is 35.5. (i) Angular quantum number determines the three dimensional shape of the orbital. Know NEET 2021 registration, exam pattern, syllabus, eligibility details & more. In which of the following pairs, the ions are iso-electronic? NEET 2021 Registration, Exam Pattern, Syllabus, Eligibility Details & More. The probability density plots of 1s and 2s orbitals are given in Fig. What is orbital angular momentum of an electron in, The orbital angular momentum of 3p electron is :-. In order not to confuse the code letter S for the orbital angular momentum with the spin quantum number S, you must examine the context in which it is used carefully. The angular momentum of an electron is zero. The result of these vector sums is specified in a code that is called a Russell-Saunders term symbol, and each term symbol identifies an energy level of the atom. Orbital angular momentum depends on __________. Which of the following statement is not correct about the characteristics of cathode rays? Check complete JEE Main 2021 exam update and other important details related to exams! (i) Both A and R are true and R is the correct explanation of A. State the result of photoelectric effect experiment that could not be explained on the basis of laws of classical physics. L-S coupling also is called R-S or Russell-Saunders coupling. and Inverse Proportions, Areas Wavelengths of different radiations are given below : The electronic configuration of valence shell of Cu is 3d, The Balmer series in the hydrogen spectrum corresponds to the transition from n. According to de Broglie, matter should exhibit dual behaviour, that is both particle and wave like properties. 3d
(c). Assertion (A) : All isotopes of a given element show the same type of chemical behaviour. For orbitals having same values of (n+l), the orbital with lower value of n will have lower energy. (iii) Electrons move in a circular path of fixed energy called orbits. Arrange s, p and d sub-shells of a shell in the increasing order of effective nuclear charge (Z. This browser does not support the video element. of Parallelograms and Triangles, Introduction Which of the following orbitals are degenerate? Orbital angular momentum of 3s and 3p are : NEET 2021 Registration, Exam Pattern, Syllabus, Eligibility Details & More. (iv) Electrons and the nucleus are held together by electrostatic forces of attraction. However, if the particle's trajectory lies in a single plane, it is sufficient to discard the vector nature of angular momentum, and treat it as a scalar (more precisely, a pseudoscalar).


text:
# Advent of Code Golf 2021 is over!

Thanks to everyone who participated in and/or helped me run the Advent of Code Golf 2021 event. It wouldn't have been so successful without the help of the community.

## Special thanks

• Everyone who solved one or more AoCG challenges: 49 users, giving 323 answers using 41 different languages!
• Everyone who left feedback in the dedicated sandbox; it would have been extra painful to QA the challenges without them, especially on my off-days.
• Everyone who posted the challenges at the right time on my off-days: lyxal (6 times!), followed by pxeger (twice) and alephalpha (once).
• Wheat Wizard who contributed three of the challenges (days 8, 15, 22).

## Statistics

The answers were given in 41 different languages.

• Many of them used popular languages (like Python or JS),
• but some were in general-purpose languages but not so popular in code golf (like Rust, C, Clojure, or Factor),
• some were given in golfing languages (05AB1E, Jelly, Vyxal, Japt, MathGolf),
• some in array languages (APL, J, BQN),
• some in plain esolangs (Whitespace, SnakeEx, Thue, Turing Machine Code),
• and even some in the answerers' own creation (ayr by ZippyMagician, Whython by pxeger).

And 49 users participated in solving the challenge, some of whom are relatively new users (the criterion being <1000 rep; I know it's arbitrary, but I don't want to dig into other users' history of activity):

• Ezhik, who solved 21 challenges in Rust! Considering the difficulty of some of the challenges and the (relative) unpopularity of the language, this is a great dedication and achievement.
• Ajax1234, who solved 16 challenges in Python. Trying and being outgolfed is a great way to learn.
• lonelyelk solved 4 challenges in Ruby, and Madison Silver solved 3 in Haskell.
• sfieger, terom, Vojket, M Virts, and wojciech-graj solved one challenge each. Welcome everyone, and we hope you enjoy solving other challenges as well!

## Scoreboards for fun :)

Here's AoC private leaderboard-style1 scoreboard for users:

                                 1111111111222222
----------------------------------------------------------------
alephalpha              *************************      25   2073
Neil                    *************************      25   1390
Kevin Cruijssen         ****************   **  **      20   1043
tjjfvi                  ***********************        23    935
Ezhik                   *********************          21    850
G B                     ************ **** ***          19    775
tsh                     *********   * ***  ** **       17    765
Ajax1234                 ****  ****** ** ****          16    720
Arnauld                 **** *  **   **  * **          12    537
loopy walt               **  ** *  ***  **  *          11    471
Dominic van Essen       * **** *** * *      *          11    456
emanresu A               *  *     **           *        5    412
ovs                     *****    ***     *              9    355
pxeger                   **       *   *  *  *           6    262
Jonah                   ** *  * **                      6    251
pajonk                   ***   * * *                    6    236
Razetime                ***     * *                     5    190
lonelyelk                      *   *     **             4    164
Jonathan Allan          *          *        *           3    158
Madison Silver                             **  *        3    125
hyper-neutrino          * *                             2     97
DLosc                    **                 *           3     97
wasif                       *     *                     2     82
AZTECCO                   **                            2     69
SuperJedi224                       *                    1     62
MarcMush                 **                             2     52
Noodle9                          *                      1     49
Anders Kaseorg                               *          1     49
caird coinheringaahing   *                              1     47
M Virts                       *                         1     46
att                                            *        1     46
wojciech-graj                 *                         1     43
Giuseppe                              *                 1     43
Unrelated String          *                             1     42
chunes                   *                              1     41
user                       *                            1     41
Vojket                     *                            1     38
ZaMoC                     *                             1     37
Xcali                         *                         1     37
sfieger                 *                               1     36
m90                               *                     1     35
terom                   *                               1     33
Engineer Toast           *                              1     29
DeathIncarnate            *                             1     29
Zaelin Goodman           *                              1     28
ZippyMagician            *                              1     27
mazzy                    *                              1     25

and here's the same for languages:

                              1111111111222222
Language             1234567890123456789012345  Solved  Score
-------------------------------------------------------------
Python               *********************          21   1688
Pari/GP              *************************      25    986
Charcoal             *************************      25    955
JavaScript           **** ** *** ****** ** **       19    784
Wolfram Language     ******************** ****      24    777
Ruby                 ************ ********          20    755
TypeScript Types     ***********************        23    751
Rust                 *********************          21    682
05AB1E               ************ **    **  **      18    650
R                    **** * *** * **     *          12    495
Jelly                *** *      *        *  *        7    321
BQN                  ***     ****     *              8    246
Java                 ** *  *  *  *  *                7    219
Retina                **       **         *          5    195
J                    **    * **                      5    166
Vyxal                 *  *      *           *        4    150
Husk                    **      *                    3    121
C                          *  *                      2     76
Perl 5                     *              *          2     70
MathGolf                  *   *                      2     65
Zsh                   *        *                     2     60
Pip                    *                 *           2     58
APL                  * *                             2     57
Japt                   **                            2     53
PHP                   *       *                      2     51
Regex                           *                    1     39
PowerShell            *                              1     37
Whython                                  *           1     37
Julia                 **                             2     36
Factor                *                              1     33
Whitespace                 *                         1     31
x86-32 machine code            *                     1     27
Clojure              *                               1     25
TI-Basic                *                            1     25
Turing Machine Code             *                    1     24
Thue                            *                    1     22
Excel                 *                              1     21
Burlesque              *                             1     21
ayr                   *                              1     19
SnakeEx               *                              1     15

The scoreboards were generated using this script.

1 Take all users participated across all challenges. For each challenge, the first solver (ordered by the posting time) gets <the number of users> score, the second gets that score minus 1, down to the last one solved. Same goes for the languages.

## Hall of Fame

• alephalpha solved all problems in Pari/GP, and most of them also in Mathematica! That's a great amount of dedication, especially given that many challenges were not so much about mathematics.
• Neil solved all problems in Charcoal (as usual), and also some fitting ones in Retina.
• tjjfvi solved most of the problems (23) in TypeScript Types (not regular TypeScript)! It is about abusing a type checker to do arbitrary calculation (not like in Turing tarpit style, but with actual numbers, strings, and arrays), something that has never been done on CGCC as far as I'm aware. Their answers may lose badly in code golf, but the effort to even write some answer in it makes them noteworthy.
• Anders Kaseorg's answer for Day 22 is interesting in its own right, as it simplifies a seemingly impossible problem into a relatively concise set of string transformations.


text:
## QRAwarrior Group Title How would you draw a cylinder for the shell method for the region that is enclosed by x = pi/2, x = -pi/2 and y = cosx? This is rotated about y = -1. 2 years ago 2 years ago

1. QRAwarrior

@FoolForMath @myininaya @experimentX @shivam_bhalla @amistre64 @Zarkon @Hero Anyone?

2. QRAwarrior

@jim_thompson5910

3. akamushi

the definite integrand of f(x)=cosx from -pi/2 to pi/2 sinx from -pi/2 to pi/2 = 1-(-1)=2

4. QRAwarrior

I do not want the answer. @akamushi

5. QRAwarrior

@FoolForMath @myininaya @experimentX @shivam_bhalla @amistre64 @Zarkon @Hero Anyone?

6. QRAwarrior

@FoolForMath @myininaya @experimentX @shivam_bhalla @amistre64 @Zarkon @Hero Anyone?

7. lgbasallote

@lgbasallote lol jk...idk shell using trig functions

8. PROSS

|dw:1337557715702:dw|

9. QRAwarrior

The height would be 2cosx, and the radius would be cosx - (-1)?

10. QRAwarrior

ie. h = 2y r = y - (-1) ?

11. QRAwarrior

|dw:1337558085638:dw|

12. QRAwarrior

The height (which are the horizontal lines of the cylinder) would be given by h = 2cosx? And the radius would be given by r = cos(x) - (-1)?

13. QRAwarrior

Wait, I think the height would be: h = 2x, due to symmetry

14. QRAwarrior

|dw:1337558202025:dw|

15. QRAwarrior

So then, radius is r = cos(x) - (-1) for sure, right?

16. QRAwarrior

And I can restate that cos(x) as y So then, r = y +1, h = 2x = 2arccos(y), I believe.

17. PROSS

now you are on the right track.

18. PROSS

if you are familiar with winplot, you can make a nice 3d representation.

19. QRAwarrior

@shivam_bhalla! Yes you finally came.

20. QRAwarrior

|dw:1337558589994:dw|

21. QRAwarrior

I have one question for either of you: I drew a vertical line from the x-axis to the function cos(x). Can that generically be represented as y?

22. shivam_bhalla

23. amistre64

x = pi/2, x = -pi/2 and y = cosx|dw:1337561871090:dw|

24. amistre64

|dw:1337562804283:dw|

25. QRAwarrior

Ok so it is: h = x y = cosx - (-1)

26. amistre64

we only need half of this, then double the results height is a measure of arccos(y) radius is from from 1 to 2 by perspective $2*2pi\int_{0}^{1}(y+1)*\cos^{-1}(y)\ dy$

27. QRAwarrior

I think I came up with this a few posts back

28. amistre64

height is a function of x; y=cos(x) arccos(y) = x = height

29. QRAwarrior

-------------------------------------------------------- Ok consider this question: Find the length of y^2 = x^3 from (0,0) to (4,8) I know the formula for arclength, but I end up getting this: |dw:1337563218324:dw|

30. QRAwarrior

|dw:1337563244465:dw|

31. QRAwarrior

How the heck can you resolve the radical when you have: |dw:1337563293983:dw| As your argument?

32. amistre64

have you tried looking at it form both forms? $\sqrt{1+(x')^2}\ or\ \sqrt{1+(y')^2}$

33. QRAwarrior

No. I think I will try the other form, BUT the problem is that I am not sure whether to pick the POSITIVE root or the NEGATIVE root..

34. amistre64

for the most part, i think you stick with the positive root

35. QRAwarrior

Why do you say "most part"

36. amistre64

distance tends to be a measure in absolute value, so the positive root seems most apt

37. QRAwarrior

WOW! I just realized how EASY it is doing it wrt x.

38. QRAwarrior

|dw:1337563549037:dw|

39. QRAwarrior

Easy U-sub. Thanks a lot amistre64. What level of education is your mathematics?

40. QRAwarrior

I was just curious

41. amistre64

i dunno what level it is, im guessing its at least on a 3rd grade level ;)

42. QRAwarrior

Ok anyways, thanks for your help

43. amistre64

youre welcome. Levelwise is difficult since im self taught for the most part of this stuff


text:
Inteference NAT Level - 2

# Inteference NAT Level - 2

Test Description

## 10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Inteference NAT Level - 2

Inteference NAT Level - 2 for Physics 2023 is part of Topic wise Tests for IIT JAM Physics preparation. The Inteference NAT Level - 2 questions and answers have been prepared according to the Physics exam syllabus.The Inteference NAT Level - 2 MCQs are made for Physics 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Inteference NAT Level - 2 below.
Solutions of Inteference NAT Level - 2 questions in English are available as part of our Topic wise Tests for IIT JAM Physics for Physics & Inteference NAT Level - 2 solutions in Hindi for Topic wise Tests for IIT JAM Physics course. Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free. Attempt Inteference NAT Level - 2 | 10 questions in 45 minutes | Mock test for Physics preparation | Free important questions MCQ to study Topic wise Tests for IIT JAM Physics for Physics Exam | Download free PDF with solutions
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*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 1

### A Michelson interferometer is configured as a wave meter as shown in the figure below may be used to compare the wavelengths of 2 laser with high precision when the mirror is the right arm of the interferometer is translated through a distance d, 1,00,000 interference fringes pass across the detector for green light and 85,865 fringes pass across the detector for red (λ = 632.82 nm) light. What is the wavelength of the green laser light in nm?

Detailed Solution for Inteference NAT Level - 2 - Question 1

λred = 632.82 nm

λred $>$ λgreen → (D) and (E) are FALSE.
Constructive path difference = Nλ

Ngλg Nrλr

λg NrλNg

= (85,865 × 632.82) / 100,000

≈ (8.6 × 10× 6.3 × 102) / 105

= 541.8

= 542 (approx)

*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 2

### Light from a laser falls on a pair of very narrow slits separated by 0.5 μm & bright fringes separated by 1.0 mm are observed on a distant screen if the frequency of the laser light is doubled, how much times the separation of the bright fringes decrease(answer in integer) ?

Detailed Solution for Inteference NAT Level - 2 - Question 2

The single slit interference equation for bright fringes is given by  (for small angles) where d is the width of the slit & in is an integer.
Since c = λv  one can relate the above equation to get
Increasing frequency would decrease the angle thus, the fringes would get closer together. Increasing the frequency by a factor of 2 would decrease the separation by 2.

*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 3

### A gas filled cell of length 0.5 cm is inserted in one arm of the michelson interferometer as shown in the figure below. The interferometer is illuminated by light of wavelength 500 nm. As the gas is evaluated from the cell, 40 fringes cross a point in the field of view. Find the refractive index of this gas

Detailed Solution for Inteference NAT Level - 2 - Question 3

Δ= 5 cm = 5 × 10−2 m
ΔN = 40 fringes
λvac = 500 nm  = 5 × 10−7 m

40 = [2(5 × 10−2)/(5 × 10−7)](n − 1)
40 = (2 × 105)(n − 1)
40/(2 × 105) = n − 1
2 × 10−4 n − 1
n = 0.0002 + 1 = 1.0002

*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 4

Blue light of wavelength 480 nm is most strongly reflected from a thin film of oil on a glass slide when viewed near normal incidence. Assuming that the index of refraction of the oil is 1.2 & that of glass is 1.6, what is the minimum thickness of the oil film in nm (other than zero)?

Detailed Solution for Inteference NAT Level - 2 - Question 4

Assuming the boundaries are vacuum-oil, oil-glass, then there will be a phase shift at the vacuum oil boundary since the refractive index of vacuum nvac < noil  & another phase shift at the oil glass boundary because noil nglass That tells us that constructive interference happens for integer wavelength mλ.
Light crosses a distance d in  but since its speed is lower in oil,

Then

∴ The condition for constructive interference becomes 2 noild = mλ
The next minimum thickness other than zero is when m = -1
So,

*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 5

In a double slit interference experiment d is the distance between the centres of the slits and w is the width of each slit. Find the minimum integer ratio d/ω for which an interference maximum of incident plane waves on a distant screen will be missing.

Detailed Solution for Inteference NAT Level - 2 - Question 5

We need a minimum of the single slit diffraction to coincide with a maximum of the double slit interference pattern (which result in a missing interference maximum)

[angulars location of minima of single slit diffraction]

[Angular locations of the maxima of double slit interference]
Ratio of 2 equations gives

So, minimum integer ratio is 2/1

*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 6

It is necessary to coat a glass lens with a non reflecting layer if the wavelength of the light in the coating is λ, the best choice is a layer of material having an index of  refraction between those of glass & air and a thickness of what fraction of  λ ?

Detailed Solution for Inteference NAT Level - 2 - Question 6

In order for the thin film layer to be non reflecting, it must cancel the reflected wavelength as in a destructive interference the change in wavelength as

Since, the wave changes phase by π at the interface below air and the coating, and again at the second interface below coating and glass
(Assume nair < ncoating < nglass). Destructive interference is thus given by a half integer wavelength change mλ/2 where the smallest change is

*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 7

Consider two horizontal glass plates with a thin film of air between them. Find the minimum value of the thickness of the film in nm of air for which the film as seen by the reflected light will appear bright if it is illuminated normally from above by blue light of wavelength 485 nm?

Detailed Solution for Inteference NAT Level - 2 - Question 7

For a thin film of thickness t, one can easily find the condition for interference phenomenon. Since the light has to travel approximately 2t to get back to the original incidence interface, one has 2t = mλ. However, since the light changes phase at the interface between air & glass, the condition for constructive interference becomes,

Minimum thickness

*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 8

Two coherent monochromatic light beams of intensities l and 4l are superposed. What is the minimum possible intensities in the resulting beam?

Detailed Solution for Inteference NAT Level - 2 - Question 8

Minimum intensity Imin=(√I− √I2)2
(√I − √4I)2
= I

*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 9

The screen of a pinhole camera is at a distance D from the pinhole. Which has a diameter d the light has an effective wavelength For what value of d in terms of   will the image be sharpest

Detailed Solution for Inteference NAT Level - 2 - Question 9

The key equation involved is
For small angles,
This blur is due to both the size of the hole and the diffraction, the arc length of the diffraction is approximately
where the factor of 2 comes from the fact that the arc length angle is symmetrical about the diffraction axis, thus twice the diffraction angle.
Define Blur equation taking the first derivative, w.r.t.
to d

*Answer can only contain numeric values
Inteference NAT Level - 2 - Question 10

A student prepared a young’s double slit by drawing two parallel lines (with a separation less than a millimeter) on a smoked glass plate. Accidently, he used two different pins to draw the lines so that the widths of the slits (regions from where smoke was removed by the pin) were in the ratio 4:1. What will be the ratio of the interference maximum to that at the interference minimum?

Detailed Solution for Inteference NAT Level - 2 - Question 10

The ratio of intensities of light proceeding from the slits, I1: I2 = 4 : 1

Therefore, the ratio of amplitudes of light proceeding from the slits,

a1:a2 = √I1: √I2 = 2:1

The amplitudes at the maximum and minimum of the interference pattern are therefore in the ratio (a1+a2) : (a1–a2) = 3:1

The intensities at the maximum and the minimum are in the ratio32:12 = 9:1

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text:
Contest Duration: ~ (local time) (100 minutes) Back to Home
A - Grouping 2 /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

ある学校には、N 人の生徒がいます。

あなたは、2 人以下のグループだと効果的な話し合いが出来ないと考えており、なるだけ多くのグループを 3 人以上にしたいです。

### 制約

• 1 \leq N \leq 1000
• 入力は全て整数

### 入力

N

### 出力

3 人以上のグループを最大で x 個作れるとき、x を出力せよ。

### 入力例 1

8

### 出力例 1

2

### 入力例 2

2

### 出力例 2

0

どのように生徒たちを分けても 3 人以上のグループを作れない場合もあります。

### 入力例 3

9

### 出力例 3

3

Score : 100 points

### Problem Statement

There are N students in a school.

We will divide these students into some groups, and in each group they will discuss some themes.

You think that groups consisting of two or less students cannot have an effective discussion, so you want to have as many groups consisting of three or more students as possible.

Divide the students so that the number of groups consisting of three or more students is maximized.

### Constraints

• 1 \leq N \leq 1000
• All input values are integers.

### Input

Input is given from Standard Input in the following format:

N

### Output

If you can form at most x groups consisting of three or more students, print x.

### Sample Input 1

8

### Sample Output 1

2

For example, you can form a group of three students and another of five students.

### Sample Input 2

2

### Sample Output 2

0

Sometimes you cannot form any group consisting of three or more students, regardless of how you divide the students.

### Sample Input 3

9

### Sample Output 3

3


text:
# Let P be an arbitrary point having sum

Question:

Let $P$ be an arbitrary point having sum of the squares of the distance from the planes $x+y+z=0, l x-n z=0$ and $x-2 y+z=0$ equal to 9 . If the locus of the point $\mathrm{P}$ is $\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{z}^{2}=9$, then the value of $l-\mathrm{n}$ is equal to________.

Solution:

Let point $\mathrm{P}$ is $(\alpha, \beta, \gamma)$

$\left(\frac{\alpha+\beta+\gamma}{\sqrt{3}}\right)^{2}+\left(\frac{\ell \alpha-\mathrm{n} \gamma}{\sqrt{\ell^{2}+\mathrm{n}^{2}}}\right)^{2}+\left(\frac{\alpha-2 \beta+\gamma}{\sqrt{6}}\right)^{2}=9$

Locus is

$\frac{(x+y+z)^{2}}{3}+\frac{(\ell x-n z)^{2}}{\ell^{2}+n^{2}}+\frac{(x-2 y+z)^{2}}{6}=9$

$x^{2}\left(\frac{1}{2}+\frac{\ell^{2}}{\ell^{2}+n^{2}}\right)+y^{2}+z^{2}\left(\frac{1}{2}+\frac{n^{2}}{\ell^{2}+n^{2}}\right)+2 z x\left(\frac{1}{2}-\frac{\ell n}{\ell^{2}+n^{2}}\right)-9=0$

Since its given that $x^{2}+y^{2}+z^{2}=9$ After solving $\ell=\mathrm{n}$

Leave a comment


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# What is the correct Marlin firmware setting for Tevo Tarantula with MKS Base V1.2 board

I am trying to correct the x&y offsets in the Tevo Tarantula that I got from a friend in order that my printer is not printing over the end. What I got so far is that I need to measure and then enter the offsets into my configuration.h file, build the firmware and flash it to the board.

Because I do not have and can not find the original firmware I found the repository from Jim Brown for the Tarantula.

Looking into the top section of the config file provided by the repo, the board configured is

#define MOTHERBOARD BOARD_MKS_GEN_13        // Original controller board with built in stepper drivers. Works with MKS BASE 1.3, 1.4

However since the board in my Tarantula has 1.2 on it I checked the boards.h file for MKS but could not find the v1.2 :

#define BOARD_MKS_BASE          40    // MKS BASE v1.0
#define BOARD_MKS_BASE_15       405   // MKS v1.5 with Allegro A4982 stepper drivers
#define BOARD_MKS_BASE_HEROIC   41    // MKS BASE 1.0 with Heroic HR4982 stepper drivers
#define BOARD_MKS_GEN_13        47    // MKS GEN v1.3 or 1.4
#define BOARD_MKS_GEN_L         53    // MKS GEN L
#define BOARD_MKS_GEN_L_V2      54    // MKS GEN L V2
#define BOARD_ZRIB_V20          504   // zrib V2.0 control b

Any idea, what board configuration would be compatible for 1.2? Or is there any other way to correct the x&y offsets other then compiling them into the firmware?

The MKS Base v1.2 is basically an Arduino MEGA2560 and a RAMPS1.4 on a single board.

You can use the RAMPS pin designation.

Note that the endstop to origin distances is explained in question How to center my prints on the build platform? (Re-calibrate homing offset).

In Jims Marlin fork you can find this at:

#define X_MIN_POS 0 - XTRA_BED_LEFT

and

#define Y_MIN_POS 0 - XTRA_BED_BACK

Unfortunately, XTRA_BED_LEFT and XTRA_BED_BACK are defined as zero; this implies that the endstops define the origin (not likely) or it is left as an excercise for you to find out. This answer explains how you figure that out.

• Thank you for the answer. For the RAMPS 1.4 the boards.c file also has multiple configurations. The board itself has 3 blue power outputs E0, E1, Fan followed by a green power output for the bed. #define BOARD_RAMPS_14_EFB 43 // RAMPS 1.4 (Power outputs: Hotend, Fan, Bed) #define BOARD_RAMPS_14_EEB 44 // RAMPS 1.4 (Power outputs: Hotend0, Hotend1, Bed) #define BOARD_RAMPS_14_EFF 45 // RAMPS 1.4 (Power outputs: Hotend, Fan0, Fan1) #define BOARD_RAMPS_14_EEF 46 // RAMPS 1.4 (Power outputs: Hotend0, Hotend1, Fan) #define BOARD_RAMPS_14_SF 48 // RAMPS 1.4 (Power outputs: Spindle, Fan
– Eike
Dec 29 '20 at 16:45
• @Eike Looks like you have the EFBE option.
– 0scar
Dec 30 '20 at 2:13
• Just greped through the source files for the Easyconfig 1.1 and 2.0 and found only references in some pins_RAMPS files to the EFBE option: ./Marlin/pins_RAMPS.h: #else // Non-specific are "EFB" (i.e., "EFBF" or "EFBE") sorry for being blind but I am stil not sure what board I should put into the config?
– Eike
Dec 30 '20 at 10:07
• @Eike EFB is a standard option, the EFBE is an added extra extruder (I understood you had 2 from your comment, but if you are only using 1, you can go for EFB).
– 0scar
Dec 30 '20 at 13:02


text:
Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

Chapter 8 - Polynomials and Factoring - 8-7 Factoring Special Cases - Practice and Problem-Solving Exercises - Page 527: 33

Answer

$(8q+9)(8q-9)$

Work Step by Step

$64q^{2}-81=$ ...write each term as a square. $=(8q)^{2}-9^{2}$ ...factor using the rule for a difference of two squares. ($a^{2}-b^{2}=(a+b)(a-b),\ a=8q,\ b=9$) $=(8q+9)(8q-9)$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
Research

Climate Change Impacts on Energy Systems

How does climate change impact a renewable energy system?

Probabilistic Forecasting

How can we reliably predict time series in complex systems under uncertainty?

Statistical, Physical Information and Modularity

How can we include statistical information such as seasonality, trends or concept drifts into DNNs to improve forecasting?

Demand Side Flexibility & Markets

How can we recognise, promote and use flexibility on the demand side?


text:
# Exercises: Oceanic heat and melting ice

The ice shelves in the Amundsen Sea are melting relatively quickly since warm water is entering the cavity beneath the ice. We thus want to know how much heat the water on the continental shelf contains, and how much heat that is entering the ice shelf cavity. The heat content is given relative to a reference temeprature $$T_{ref}$$. What you calculate, is how much heat you have to remove before the temperature of the water is $$T_{ref}$$. If you have to add heat for the water to reach $$T_{ref}$$, then the heat content is negative.

We can find the heat content $$H$$ in the water from a CTD-profile (observations of temperature, and salinity from the surface to the bottom):

$$H\approx\sum_{z=1}^{depth}\rho c_p \left(T(z)-T_{ref}\right)\Delta z$$

$$\rho$$ is the density of the water (about 1027 kg/m$$^3$$ and $$c_p=4\times10^3$$J/kg/C is its heat capacity.

You are free to choose the reference temperature – but since sea water freezes and -1.9C it is practical to choose $$T_{ref}$$=-1.9C. The heat content is then the energy one can remove from the water before it freezes. $$H$$ is the heat conent per square meter.

When warm water is in contact with ice the heat will be used to melt ice. To melt a kilo of ice you need approximately 330 kJ (or a bit more if the ice is cold).

## Exercise 1

1. Import the data from the CTD-profiles from the Amundsen Sea (you’ll find them one after each other in the file ENG_CTDdata_Amundsenhavet in Geogebra. Plot a few of the profiles and calculated the heat content
2. How much of the heat is found in the upper 200 m? below 200 m depth?
3. We are mostly interested in the heat at depth. Do you know why?
4. Make a table where you note the heat content (in the upper and lower layer separately) and the temperature at the bottom. (You may well cooperate in groups!)
5. My colleagues argue that there is a direct relationship between the bottom temperature and the heat content, so that all we’d need to measure is the temperature at the bottom. What does it look like in your data? Can you draw a conclusion based on the data at hand? Discuss!

If you want to add more points to your table, you can download data from the entire cruise in 2010 from NODC, a large data bank where we scientist send our data so that other researchers (and you!) can use them!

## Exercise 2

1. How much ice (per square meter) can we melt with the heat from the profiles above?
2. The melt below the ice shelf in the Amundsen Sea is about 400 Gton per year. How much heat is that?

## Exercise 3

1. If the West Antarctic Ice sheet were to collapse, the sea level would increase with three meters – how many cubic meters of ice does that correspond to?
2. How much heat is needed to melt that ice? (Does it have to melt for the sea level to rice?)
3. A wind turbine typically produce 2 MW – how long time would it take for the wind turbine to produce the energy needed to melt the ice?
4. The earth receives about 0.5 W/m$$^2$$ more energy (through radiation) from the sun than what is given off – how long time would it take to melt the ice if all of the energy was used to melt ice?
5. A Norwegian uses about 30 000 kWh per person per year –how many cubic meters of melted ice does that correspond to?

[slr-infobox]
Radius of the Earth: 6371 km

Density, ice: 900 kg/m$$^3$$

Density, snow: 900 kg/m$$^3$$

Density, sea water: 1027 kg/m$$^3$$

Percentage of the Earth that is water: 70%
[/slr-infobox]


text:
# Integrating logarithms

Calculus Level 4

$\large \int_0^\infty \dfrac{\ln(1+x^2)}{(1+x^2)}\; dx$

If the value of the above integral can be written as $A\pi\ln(B)$ for positive integers $A$ and $B$, then enter the value of $10A+11B$.

×


text:
# How to make double cline in tables?

I want to draw a double cline in a table where the first column is multirow With double \hline I can draw a full double horizontal line but double \cline{i-j} seems to have the same effect with single \cline. Is there any other special command to do that?

Thank you

-

AFAIK the \cline does not add vertical space by itself, therefore the two are just printed over each other. The booktabs package, which I can recommend greatly in general for all tables, defines therefore the \morecmidrules macro:

% \cline is now \cmidrule
\cmidrule{1-2}\morecmidrules\cmidrule{1-2}

However, the booktabs manual says that double lines are evil and should not be used at all....

-
Thanks, good hint but now I have a different problem. The vertical lines-borders of the table are broken. Please see the image: img189.imageshack.us/img189/8383/brokentable.png –  Vasilis Feb 3 '11 at 0:17
@Vasilis: Mmm, I can't tell how to fix that. All what I know is that vertical lines are also considered as evil by the booktabs manual ;-) My advice is to avoid them and most horizontal lines. Only do a \toprule on top and a \bottomrule at the bottom, plus a single \cmidrule where you wanted the double rule. This design is new to most people which know tables only from M\$ Word, but believe me, it looks better! –  Martin Scharrer Feb 3 '11 at 0:33
@Vasilis. As Martin says, the table you've linked to should not have vertical lines. –  Joseph Wright Feb 3 '11 at 6:47
Indeed it looks better without vertical lines. –  Vasilis Feb 3 '11 at 14:35

use package hhline, available with any TeX distribution:

\documentclass[a4paper]{article}
\usepackage{hhline}
\begin{document}

\begin{tabular}{ccc}\hhline{=~~}
foo & bar & baz  \\\hhline{~=~}
foo & bar & baz  \\\hhline{~~=}
\end{tabular}

\end{document}

-


text:
# Loop invariant initialisation confusion

Consider the algorithm LastMatch below, which returns the offset (shift) of the last occurrence of the pattern P in text T, or -1 if P does not occur in T:

LastMatch(T,P)
for(s = T.length - P.length downto 0)
j = 1
while(j =< P.length and P[j] == T[s + j])
j++
if(j == P.length + 1)
return s
return -1

I've been given a loop invariant for the while loop:

$$\forall k(1 \leq k

The initialisation of this invariant confuses me. Before we enter the while loop, $$j=1$$. So we're asking is there a $$1\leq k<1$$ such that $$P[k] ==T[s+k]$$?

I cannot find a $$k$$ which satisfies this inequality, so I do not understand what this is saying. So why is the invariant satisfied before we enter the loop? Is it because when I cannot find a $$k$$ it implies that $$P[k]$$ and $$T[s+k]$$ are both equal to the empty set?


text:
# What does 9 to the power of 1/2 mean?

## What does 9 to the power of 1/2 mean?

A Universal Rule Raising 9 to the 2nd power gives you 81. Now you have to get the 1st root of 81. But the 1st root of any number is the number itself, so the answer remains 81. Now look at the expression 9^1/2. So all you have to do is get the square root of 9, which is 3.

## What does the power of 1/2 mean?

Fractional exponents Taking a number to the power of 12 undoes taking a number to the power of 2 (or squaring it). In other words, taking a number to the power of 12 is the same thing as taking a square root: x1/2u221ax

## How do you do a 1/2 exponent?

Hence x to the power of 1/2 can be written as x(1/2) which is a fractional exponent. Where the number x is called the base, whereas (1/2) is the power or exponent of the expression. Any exponent of (1/2) is actually the square root of that number.

## How do you solve a fraction to a power?

How To Solve Fractional Exponents?

• Rule 1: a1/m xd7 a1/n a. (1/m + 1/n)
• Rule 2: a1/m xf7 a1/n a. (1/m – 1/n)
• Rule 3: a1/m xd7 b1/m (ab) 1/m
• Rule 4: a1/m xf7 b1/m (axf7b) 1/m
• Rule 5: a-m/n (1/a) m/n
• ## What is 1 2 to the power of 4 as a fraction?

Fractional exponents Taking a number to the power of 12 undoes taking a number to the power of 2 (or squaring it). In other words, taking a number to the power of 12 is the same thing as taking a square root: x1/2u221ax

## What does to the power of 0.5 mean?

Hence x to the power of 1/2 can be written as x(1/2) which is a fractional exponent. Where the number x is called the base, whereas (1/2) is the power or exponent of the expression. Any exponent of (1/2) is actually the square root of that number.


text:
# Is a larger beta weight a better predictor than a high t-statistic?

Say there are two variables. Variable A has a higher $\beta$ weight than variable B but variable B has a higher t-statistic than variable A. Can either of these measurements, standardized $\beta$ or t-value, offer better predictive power over the other? Must t-value and $\beta$ be taken into consideration together or not?

• Could you tell us what you mean by "predictive power" and what "better" means?
– whuber
Mar 16, 2013 at 3:04

It would help if you could answer @whuber's question. However, in general, this question cannot be answered.

The reason is that variables are almost always on incommensurate scales. Consider the typical study that involves human subjects (as in medical research or the social and behavioral sciences), what covariates do we typically have? It is quite common to include $\text{sex}$, $\text{age}$, $\text{weight}$, $\text{height}$, etc. Now ask yourself: How many years makes you male? How many centimeters equals a kilogram? Etc. These cannot be equated. However, the ability of knowledge of one variable to help you differentiate amongst possible values of another variable is a function not only of the slope of the relationship between the two variables in question, but also of how spread out those values are1. That is, you cannot elide the issue of the incommensurable units with which your variables are measured. Thus, @StocSim's answer, while commonly believed, will not work: the significance of your variables (their p-values, t statistics, etc.) is related to how spread out those variables are in your dataset and there is no absolute2 way to determine whether the range of your $\text{heights}$ is comparable to the range of your $\text{ages}$.

1 See my answer here: how-do-you-interpret-a-low-coefficient-yet-statistically-significant-with-a-high, for more along these lines.
2 It may be possible to equate variables by recourse to something else, e.g., how much it would cost to increase the amount of different variables. Note, however, that this will change over time with changes in technology, the market, etc.

• Also consider what happens to your $\beta$ if you measure peoples heights in millimeters, or meters. Aug 28, 2013 at 23:57

$\beta$ and t-stat tell very different bits of information about a variable's effect in a statistical model and they are not exchangeable:

• $\beta$ (standardized effect size) is far more important. It tells how strong or meaningful the effect is. B (unstandardized effect size) is usually easier to interpret and so is preferred to explain what the results actually mean in real-world terms, but $\beta$ (standardized effect size) is more useful for comparing the relative strength of effects between various variables, since the B measures are on different scales.
• t-stat (statistical significance) is also important, but it only tells you how reliable the measure of $\beta$ is. That's all it does. It absolutely does not tell you how important a variable is, and although it is very, very widely misused in that way, that is a misuse. (The same, of course, applies not only to the t-stat, but to all measures of statistical significance.)

Taken together, the $\beta$ and t-stat give you the effect size and how reliable is the estimation of the effect size. There are four general possible scenarios:

1. High $\beta$ and signficant t-stat: The high $\beta$ means that the variable is indeed important and the significant t means that you can trust that the high $\beta$ is reliable.
2. High $\beta$ but insignficant t-stat: The high $\beta$ means that the variable is possibly important, but the insignificant t means that you cannot trust this result because your sample size is too small for you to be confident in the results.
3. Low $\beta$ but signficant t-stat: The low $\beta$ means that the variable is not important and the significant t means that you can trust that the low $\beta$ is reliable.
4. Low $\beta$ and insignficant t-stat: The low $\beta$ means that the variable is possibly not important, but the insignificant t means that you cannot trust this result because your sample size is too small for you to be confident in the results. However, since an unimportant effect of the variable would require a very large sample to register a significant t, if the sample is reasonably large and $\beta$ is quite low, it is reasonable to conclude that the variable probably has very little, if any, effect.

In an ideal world, all t-stats should always be statistically significant; if you have a huge sample size, then this should always be the case. In practice, the harder it is to collect the data, the harder it is to get a large sample size. Thus, #4 (low $\beta$, insignficant t) is often interpreted as a low or non-existent effect. However, if the sample size is not sufficiently large, then #2 (high $\beta$, insignficant t) cannot be ruled out as a non-existent effect. It simply means that your sample size isn't large enough for you to be sure, but there might indeed be an effect.

• Wording of your answer could be misleading. As far as I remember, SPSS uses B for regression parameter and Beta for standarized parameter. On another hand, R uses Estimate for parameter and t value for standarized parameter. What you call "t stat" is rather a $p$-value, since $t$-statistic in case of regression is parameter/se(parameter) i.e. Wald's $t$ statistic (see stats.stackexchange.com/questions/56066/… )
– Tim
Jul 8, 2016 at 14:58
• No, what I call "t stat" is the t-statistic. I agree with you that the p-value is a more generalized version of what I am talking about, but I am simply using the same terminology used by the original poster. Jul 11, 2016 at 15:22

You're getting at two distinct concepts:

1. Statistical significance
2. Material significance, some notion of practical significance.

In economics, people call number (2) economic significance. In biology, I imagine they call it biological significance.

Statistical significance can be seen from the p-value (assuming your standard errors etc... are done properly). Material significance, economic significance is a more field, problem specific question.

• Is a 0.05% difference in return materially important? Almost certainly no for high risk venture capital investing, but almost certainly yes for short term rates on near risk free securities.
• Is aerodynamic drag requiring 5 watts of power at 25 mph materially important? Almost certainly not for a car, but quite possibly yes for a pro racing cyclist.

Does a big number imply material significance?

• Of course not because you can always make a number big by measuring in tiny units!

What if you standardize a variable by its standard error, making the estimated coefficient at least invariant to units?

• This may be better, but as @Gung discusses, it still doesn't answer how this effect relates to other effects. Is the $\beta$ in question measuring the effect of a small brook flowing into the Niagra river while the massive Niagra falls is nearby?

Answering the question of whether an effect is materially important is inherently field and problem specific. Generally speaking, you want to capture the materially important effects when forecasting.

Beta weight itself does not say much.You should also consider its standart deviation, therefore t statistic is better for you to understand which variable(a or b) has a greater effect.


text:
During 2 hours one winter afternoon,when the outside temperature was 10° C, a househeated by electricity was kept at 22° C with theexpenditure of 46 kwh(kilowatt·hours) of electric energy.
(a) What was the average energy leakage in joules per second(watts) through the walls of the house to the environment (theoutside air and ground)?
watts

(b) The rate at which energy is transferred between two systems dueto a temperature difference is often proportional to theirtemperature difference. Assuming this to hold in this case, if thehouse temperature had been kept at 25° C(77° F), how many kwh of electricitywould have been consumed?
kwh


text:
Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case.(English)Zbl 1282.35088

In this very nice paper under review and following previous papers due to the authors in the radial case, they consider type II blow-up solutions to the energy-critical focusing wave equation. The result reads as follows: Let $$W$$ be the unique radial positive stationary solution of the equation. Up to the symmetries of the equation, under a suitable smallness assumption, any type II blow-up solution is asymptotically a regular solution plus a rescaled Lorentz transform of $$W$$ concentrating at the origin.

MSC:

 35B44 Blow-up in context of PDEs 35L71 Second-order semilinear hyperbolic equations 35B33 Critical exponents in context of PDEs

Keywords:

rescaled Lorentz transform
Full Text:

References:

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