Topic 7: Multiple Linear Regression

Question 1

What extra assumptions are introduced in multiple variable regression?

Answer 1

• No exact collinearity between X variables
• No specification bias

Question 2

What does an estimate in multiple linear regression mean?

Answer 2

The change in Y caused by a change in x, holding all other variables constant

Question 3

How does the correlation between regressors affect the error of the estimates

Answer 3

Greater the correlation, higher the error

Question 4

Why do we use Adjusted R^2?

Answer 4

Because normal R^2 can be increased just by adding junk regressors. Adjusted R^2 compensates for the number of variables

Question 5

When can we compare R^2 values?

Answer 5

• When sample size is the same
• When dependant variables are the same

Question 6

Give the formula for adjusted R^2

Answer 6

Question 7

Does R^2 have any intrinsic properties that might favour its use over other calculations?

Answer 7

Nope, pretty arbitrary

Question 8

What is the Gross/Simple correlation coefficient?

Answer 8

Shown as r_1-2, where 1 = Y and i > 1 = Xi. Shows the correlation between two variables

Question 9

What is the partial correlation coefficient?

Answer 9

The correlation between two variables, eliminating the correlation effect from some other variables. Shown as r₁₂.₃₄, where the effects from 3 and 4 are eliminated