Q1:

The estimation results are the following (sample size is 16):

Q=130-1.12X₁+0.04X₂+0.90X₃-0.04X₄

Where X₁ is price, X₂ is income, X3 is advertising, and X₄ is the price of related good

Explained sum of squires=946.181 and residual sum of squires=49.773

Answer the following questions:

A.Interpret the estimated regression equation.

B.What is the value of coefficient of determination? Interpret the value.

C.What is the value of adjusted coefficient of determination? Interpret the value.

D.What is the value of coefficient of correlation? Interpret the value.

E.Is the overall regression model significant? Test at the 5% level of significance.

Q3: The following are two different samples with two independent variables each of them in order to investigate the behavior of Y (dependent variable):

SAMPLE 1

SAMPLE 2

Observation

Y

X1X2

Z1Z2

1

1

24

24

2

4

612

612

3

2

411

48

4

3

713

713

A.Identify the multicollinearity problem in any of the two samples. Justify your answer.

B.Explain the consequences in your OLS estimations in the presence of multicollinearity in each sample.

C.Explain the strategies that you would use in order to solve the problem in each sample.

Q4:

Y

X1

X2

11

20

8.1

16

18

8.4

11

22

8.5

14

21

8.5

13

27

8.8

17

26

9.0

14

25

8.9

15

27

9.4

12

30

9.5

18

28

9.5

Using the data given above, answer the following:

A.Estimate the multiple linear regression equation of Y on X1, X2 and interpret the results.

B.Test at the 5 percent level for the statistical significance of the each slope coefficient.

C.Find the coefficient of determination and interpret the results.

D.Test at the 5 percent level for the overall statistical significance of the regression.