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**"Simple linear regression model:**

Y = β

E(Y) = β

A linear model means that it is linear in β's, and

The independent variable X could be W

Y = β

_{0}+ β_{1}X + εE(Y) = β

_{0}+ β_{1}XA linear model means that it is linear in β's, and

*not*necessarily 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

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

Y = β

_{0}+ β_{1}X_{1}+ β_{2}X_{2}+ ... + β_{k}X_{k}+ εIf 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!