# Tagged Questions

Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.

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1answer
180 views

### Can someone explain what plim is?

In my Introductory Econometrics class we discussed a concept of "plim" or "probability limit. I'm not sure what this means though and my professor doesn't explain it well at all. Can someone tell me ...
1answer
18 views

### Second order least squares problem with one parameter

I want to fit a set of measured data $x_i$ and $y_i$ to the expression: $$\beta^2 + \beta x_i = y_i$$ $\beta$ is my only free parameter. Although this is a really simple expression, the standard ...
1answer
55 views

### Finding the value which minimises all residuals

I have a series of observations, measurements made at various times $t$. I now need to determine the most likely value of $R$ (distance) using the model below. The guide says I should find the value ...
1answer
150 views

### Recursive curve fitting

I have a few points for which I have to obtain a best fit. (I tried to use the least squares curve fitting method as Robert says, however, since it seems to be fitting rather poorly, any other ...
1answer
74 views

### Why Logistic Regression for Classification Problems?

In a class on machine learning, we covered classification problems. In such a problem, you are studying a property of some object, say malignity of tumors in a patient. You are first given a training ...
1answer
24 views

### Optimization, solving for the 'error' coefficient

Given a modified regression equation: $\hat Y = \exp(\beta_0 + \sum\beta_ix_i + \varepsilon)*F$ where: $\hat Y = 11353$ $\beta_0 = 8.693021$ $\sum\beta_ix_i = 5.95487177696$ $F = 0.21829$ what ...
2answers
182 views

### Overcoming Linear Regression Assumptions

I'm a beginner in econometrics (learning on my own, and not from school) and I'm trying to build an intuition to understanding linear regression. We know that modeling real world data is bound to ...
1answer
48 views

### P-value not shown when there are too many variables in a linear regression

x<-c(1,2,3) y<-x^1.1+x summary(lm(y~x+I(x^1.1))) I have this code in R but it just is for the sake of easier understanding of what I am trying to achieve. ...
1answer
85 views

### How to convert the constants in a regression equation to constants in a linear equation

Hello dear mathematicians, I'm not entirely sure what to tag this question with since I'm new here but I hope some more experienced user can guide me. Here is my problem: I'm using an internal ...
1answer
226 views

### Strange behaviour with ode45 in matlab, probably some numerical error.

I'm having a problem with a parameter estimation in a non-linear model. I think the culprit is that ode45 (an ode solver in matlab) is not properly solving my ode. It's the in red highlighted part, ...
1answer
84 views

### Linear algebra with a linear model (Matlab)

Given the equation $$r = B + e(r\cos(\theta))$$ and the corresponding data: $\theta: 0.88; 1.1; 1.42; 1.77; 2.14$ and $r: 3; 2.4; 1.65; 1.25; 1.01$ How do you input these data for matlab to ...
1answer
95 views

### Is this expression correct?

sorry I don't know how to post Latex here I have to implement in Matlab the following formula and I'd like to know if the expression given here really corresponds to the minimum indicated, and why: ...
1answer
1k views

### How to calculate hyperbola from data points?

I have 4 data points, from which I want to calculate a hyperbola. It seems that the Excel trendline feature can't do it for me, so how do I find the relationship? The points are: (x,y) (3, 0.008) ...
1answer
354 views

### How do I fit a model with piecewise linear regression

I have a set of points in 3D (x,y,z). I ordered these points from the lowest to highest. So, I want to used linear regression to fit a line through these ordered points and then to find out a break ...
1answer
191 views

### If the covariance of A, B if E(A) = 0, does convariance of A, B = 0?

So I have got 2 variables, $A$ and $B$. I know for a fact that $E(A)$ = 0. I don't know if they are independent. $$Cov(A, B) = E(A B) - E(B) E(A)$$ I know that $E(A) = 0$. Does that mean \$E(A B) ...
1answer
60 views

### Estimating the equation of a line from its rounded values

So, I'm playing a game where there is a certain percent value that changes over time. I look at it occasionally, it seems to be approximately linear in time. However, the change is slow enough that ...
0answers
10 views

### Calculate the tendency of a set of samples

I develop an application in which I constantly get samples of heart pulse. I defined an interval of $t$ seconds. In each $t$ seconds I have $n$ samples. In every interval, I want to calculate the ...
0answers
10 views

### FF neural network with single sigmoid output (calculation of probability)

first of all I'm sorry for my not very skilled English, but I will do my best to explain my problem. I'm trying to create a feedforward neural network with one hidden layer (with probably arctan ...
0answers
12 views

### Stata: “Between and fixed effect estimates” in a linear regression?

I'm working on a paper by B. H. Baltagi and I am trying to replicate the results. It can be found here, the data is here. I'm supposed to do a linear regression - sounds simple. The author uses Stata, ...
1answer
15 views

### Interpretation of regression formula returned by computer software

I have a dataset consisting of 744 records. Data exploring software generated an equation I don't know how to interpret in simple words. I really appreciate if you could help me about this matter. ...
0answers
27 views

### Multiple regression using excel [closed]

I'm having a project that requires forecasting using multiple regression given an excel sheet. Using the standard formula for multiple regression First, I tried to get accurate values for predictors, ...
0answers
18 views

### Multivariate analysis of High Frequency time series

Hi I have data in the following manner ...
1answer
21 views

### Multiple regression problems (restricted regression, dummy variables)

Q1. Model 1: $Y=X_1\beta_1+\varepsilon$ Model 2: $Y=X_1\beta_1+X_2\beta_2+\varepsilon$ (a) Suppose that Model 1 is true. If we estimates OLS estrimator $b_1$ for $\beta_1$ in Model 2, what will happen ...
0answers
45 views

### Generating an equation from an image I have

I am not exactly sure if this question belongs here but I could not think of a better place to ask. So I recently discovered that various people on the internet have created equations for rather ...
2answers
34 views

### Fast way of finding RSS of Multiple Linear Regression

Is there any smarter way to compute Residual Sum of Squares(RSS) in Multiple Linear Regression other then fitting the model -> find coefficients -> find fitted values -> find residuals -> find norm of ...
0answers
31 views

### If $\underset{n \times n}{M}$ is a symmetric and idempotent matrix having rank $r$

If $\underset{n \times n}{M}$ is a symmetric and idempotent matrix having rank $r$ then $$w'Mw \sim \sigma^2 \chi^2_{(r)}$$ where $\underset {n \times 1}{W} \sim N(0,\sigma^2 I)$ that is, \$w_i \sim ...
1answer
30 views

### Techniques to find regression parameters for multiple datasets where a subset of parameters should be the same for all datasets

I have five sets of observations of measured y as some function of measured $x_1, x_2, x_3,\ldots$ and I want to fit five functions to these observations. They have the form  y = f(x_1, x_2, ...
0answers
18 views

### Simple calculation problem in linear regression model

Define $$Y_i=\beta_0+\beta_1 X_i+\epsilon_i$$ $$\bar Y=\beta_0+\beta_1 \bar X+\bar \epsilon$$ $$\bar Y=\frac{\sum_{i=1}^{n} Y_i}{n}$$ $$\bar X=\frac{\sum_{i=1}^{n} X_i}{n}$$ \bar ...
0answers
40 views

### What is the difference between random and nonrandom?

In a simple regression model $Y_i=\beta_0+\beta_1 X_i+\epsilon_i$, $X_i$ is nonrandom. But we don't know $\beta_0, \beta_1$ value (we should estimate them in our model), $Y_i$ is random. I wonder what ...
0answers
28 views

### how to determinte 3 parameter by best fitting?

I have a bunch of experimental data given by someone else which should fitting into the following form $$y = A\exp(-b/(x-\mu))$$ where $A$, $b$ and $\mu$ are constant but not known. I am ...
0answers
40 views

### Omitted Variable Bias?

The question is more involved on how to calculate the omitted variable bias. We were given data and are supposed to use SAS to run regression models. First, how do you know if results suggests there ...
0answers
18 views

### Trouble following this derivation regarding linear regression

$$\displaystyle \sum_{i =i}^n e_i^2 = \displaystyle \sum_{i =1}^n ((v_i - au_i) - (b - \bar{y} + a \bar{x}))^2$$  \displaystyle \sum_{i =i}^n e_i^2 = \displaystyle \sum_{i =1}^n(v_i - au_i)^2 + ...
0answers
24 views

### Is $x_3$ important in the second model?

A data set contains $n= 32$ observations on four variables $y,x_1,x_2$ and $x_3$. Model $y=\beta_0 + \beta_1 x_1 +\beta_2 x_2 + \epsilon$ produced $R^2 = 0.8806$. But model \$y = \beta_0 + \beta_1 x_1+ ...
0answers
18 views

### Finding lines from set of 2-dimensional points

Given a set of N 2-dimensional points, how can I retrieve lines by doing some kind of clustering from the points? It guess it is a kind of regression analysis problem but I am not able to solve it. ...
2answers
223 views

### Unconditional expectation vs conditional expectation in regressions - does it really matter?

I refer here to a simple linear regression whose true representation is given by the equation: $y_i=x_i'\beta+u_i$, where as usual $x_i$ is a $Kx1$ vector of independent explanatory variables, ...
0answers
13 views

### Multivariable regression with any amount of variables

Does anyone know a general method to find the least square regression equation for any number of variables and any power? Assume that I have enough datapoints to solve for the coefficients in the ...
0answers
25 views

### Calculate the estimated residual series $\hat{u}_t = y_t + b_{OLS}$

I am struggeling with this excercise: Use this data and the simple model $y_t = β + u_t$ and calculate the estimated residual series $$\hat{u}_t = y_t + b_{OLS}$$ using the least squares estimator ...
0answers
19 views

### What's the difference between fixed design and random design?

I am thinking about the regression problem of random design. Consider the model $Y=X\beta+\varepsilon$, where $X\in \mathbb{R}^{n*p}$. I know that under the fixed design, if we have that the $i$-th ...
0answers
34 views

### Finding a closed-form formula for the variance of the absorption direct estimator

I need to solve a system of linear equations via monte carlo methods, i.e. $$Ax=B$$ I need to derive the a formula for the variance of an estimator given that the estimator is equal to: - let $Q$ be ...
0answers
48 views

### How does this affect the slope

This is a Linear regression question, where I have a list of values for Sales ($Y$) and Property ($X$), I have calculated the Mean for both $Y$ and $X$, resulting in $Y=52.2$and $X=17$, I have ...
1answer
32 views

### Minimizing a function with vectors

This is a part of a problem that I'm having, and I'm unclear how to do this particular step. I'm dealing with a ridged regression and I need to minimize the equation \sum (Y_i - \beta^Tx_i)^2 + ...
1answer
44 views

### Determining slope of line relative to a maximum

In the following scientific report (Seismic Q estimation), a mathematical procedure of linear curve-fitting is described in words. The authors state: The stratigraphic effects are minimized by ...
0answers
33 views

### Non-linear regression - least square regression

I was trying to get some insight into how to solve non-linear regression model problems. Unfortunately, I've never attended a lecture on statistical math. Here is the link: In page number 4, they ...
1answer
88 views

### How to find autoregressive coefficients of ARMA model

I am searching various sources to find the method of manually calculating coefficients of Auto Regressive Moving Average model. The following is the text I found in a book. My question is how a1 and ...
0answers
52 views

### Why Local Minimum is calculated for a derivative function instead of actual function?

In Machine learning regression problem, why the local minimum is computed for a derivative function instead of the actual function? Example: http://en.wikipedia.org/wiki/Gradient_descent The ...
0answers
29 views

### Standard deviation of a particular dimension in a multivariate Gaussian distribution

I have a set (cluster) of vectors in dimension $d$. From this I have calculated the sample mean and covariance matrix ( I make the assumption that they are from a multivariate Gaussian). My question ...
0answers
26 views

### Regression Model Estimator

Assume regression model $y_i = \alpha + \beta x_i + \epsilon_i$ with $E[\epsilon_i] = 0, E[\epsilon^2] = \sigma^2, E[\epsilon_i \epsilon_j] = 0$ where $i \ne j$. Suppose that we are given data in ...
0answers
27 views

### What to do when the predictors do not accord with common sense/literature, but the model is fine/best according to log likelihood and LRT?

down vote favorite I would try to clarify the problem and then ask the questions. The problem (variable names are masked due to confidentiality): I ran a binary logistic regression, in which there ...
0answers
22 views

### Multivariate linear regression/aproximation

I'm solving a problem which features a function $f: \mathbb{R}^4 \rightarrow \mathbb{R}^4.$ I don't know the function, but I assume it's linear and it can be expressed as \$ \mathbf{y} = \mathbf{A} ...
0answers
30 views

### differences between linear regression and generalized linear regression

I have found the R program of the linear regression for the consumer price index of a country, expressed in terms of years and quarters division. The formula obtained is: ...
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