Chapter 3:

Question 1

Simple Linear Regression Model:

Answer 1

y=Beta0+Beta1*x+u

Question 2

Population Regression Function:

Answer 2

E(y|x)=Beta0+Beta1*x

Expected value of y given a particular value of x.

Question 3

Sample Regression Function:

Answer 3

yhat=Beta0hat+Beta1hat*x

Question 4

Deriving OLS Estimates:

Answer 4

E(u)=0
E(ux)=0

y=Beta0+Beta1x+u
-> u=y-Beta0-Beta1x

Question 5

Population Moment Restrictions:

Answer 5

First: E(y-Beta0-Beta1x)=0
Second: E((y-Beta0-Beta1x)*x)=0

Question 6

Algebraic Properties of OLS:

Answer 6

1. Summation of uihat is zero
   The sum or average of OLS residuals is zero.
   First Sample Moment Restriction!
2. Summation of uihat*xi is zero
   The sample covariance between the regressor and the OLS residuals is zero.
   Second Sample Moment Restriction!