A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process.

A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).

All statistical hypothesis tests and all statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference.

Could you explain each sentence in simple terms?
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process.

A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).

All statistical hypothesis tests and all statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference.

Could you explain each sentence in simple terms?
user
1. A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population).
2. A statistical model represents, often in considerably idealized form, the data-generating process.
3. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
4. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).
5. All statistical hypothesis tests and all statistical estimators are derived via statistical models.
6. More generally, statistical models are part of the foundation of statistical inference.

I'm having trouble understanding the first sentence.

1. A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population).

I understand that a statistical model is a mathematical model that embodies a set of statistical assumptions. But what do you mean by "the generation of sample data (and similar data from a larger population)"?

I'm also having trouble understanding the second sentence.

2. A statistical model represents, often in considerably idealized form, the data-generating process.

What do you mean by "the data-generating process"?

I'm having trouble understanding the third sentence.

3. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.

What do you mean by "a mathematical relationship between one or more random variables and other non-random variables"?

I'm having trouble understanding the fourth sentence.

4. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).

What do you mean by "a formal representation of a theory"?

I'm having trouble understanding the fifth sentence.

5. All statistical hypothesis tests and all statistical estimators are derived via statistical models.

What do you mean by "derived via statistical models"?

I'm having trouble understanding the sixth sentence.

6. More generally, statistical models are part of the foundation of statistical inference.

What do you mean by "statistical inference"?

I'm having trouble understanding the seventh sentence
assistant
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process.

A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).

All statistical hypothesis tests and all statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference.

Could you explain each sentence in simple terms?
user
## Ad blocker interference detected!

### Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.
assistant
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process.

A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).

All statistical hypothesis tests and all statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference.

Could you explain each sentence in simple terms?
user
1. A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population).
2. A statistical model represents, often in considerably idealized form, the data-generating process.
3. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
4. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).
5. All statistical hypothesis tests and all statistical estimators are derived via statistical models.
6. More generally, statistical models are part of the foundation of statistical inference.

I'm having trouble understanding the first sentence.

1. A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population).

I understand that a statistical model is a mathematical model that embodies a set of statistical assumptions. But what do you mean by "the generation of sample data (and similar data from a larger population)"?

I'm also having trouble understanding the second sentence.

2. A statistical model represents, often in considerably idealized form, the data-generating process.

What do you mean by "the data-generating process"?

I'm having trouble understanding the third sentence.

3. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.

What do you mean by "a mathematical relationship between one or more random variables and other non-random variables"?

I'm having trouble understanding the fourth sentence.

4. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).

What do you mean by "a formal representation of a theory"?

I'm having trouble understanding the fifth sentence.

5. All statistical hypothesis tests and all statistical estimators are derived via statistical models.

What do you mean by "derived via statistical models"?

I'm having trouble understanding the sixth sentence.

6. More generally, statistical models are part of the foundation of statistical inference.

What do you mean by "statistical inference"?

I'm having trouble understanding the seventh sentence
assistant