Part 2 - Regression

Question 1

Explain with the use of equations, the difference between the
sample regression function and the population regression
function (standard one).

Answer 1

The population regression function is a linear function that
describes the true relationship in the population between the two
variables.
Yt = α + βXt + ut. The sample regression function is the estimate of the relationship
between X and Y based on the sample.
Yˆ
t = ˆα + βˆXt

Question 2

Do hypotheses tested concern the actual values of the
coefficients (β) or their estimated values (βˆ)?

Answer 2

β. These are unknown — not estimated, like βˆ. We need
hypotheses only because we have no way of knowing the true value
of β.