1)(adsbygoogle = window.adsbygoogle || []).push({}); "Simple linear regression model:

Y = β_{0}+ β_{1}X + ε

E(Y) = β_{0}+ β_{1}X

A linear model means that it is linear in β's, andnotnecessarily a linear function of X.

The independent variable X could be W^{2}or ln(W), and so on, for some other independent variable W."

I have some trouble understanding the last line. I was told that a SIMPLE linear regression model is always a straight line model, it is a least-square LINE of best fit. But if X=W^{2}, then we have E(Y) = β_{0}+ β_{1}W^{2}which is not a straight line...how come?? Is this allowed?

2)"A SIMPLE linear regression is a linear regression in which there is only ONE independent variable."

Now is the following a simple linear regression or a multiple linear regression?

Y = β_{0}+ β_{1}X + β_{2}X^{2}+ ε

It has only one independent variable X, so is it simple linear regression? But this just looks a bit funny to me...

3)"A linear regression model is of the form:

Y = β_{0}+ β_{1}X_{1}+ β_{2}X_{2}+ ... + β_{k}X_{k}+ ε

If there is more than one independent variable, then the model is called a MULTIPLE linear regression model."

This idea doesn't seem too clear to me. What can the X_{i}'s be? What are some actual examples of mutliple linear model? Does a linear model always have to be a straight line or a plane?

Thanks for explaining!

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