# MST 3102 university of Guyana Regression Analysis Practice Quiz

University of GuyanaFaculty of Natural Sciences

Semester I 0f 2021-22

MST 3102 (Regression Analysis)

Date and Time: Friday 11th March, 2022 10:00.

Duration: 1 hr.

Instructions to Candidates:

Answer ALL questions

1. From some statistical analysis, we have the following table

X in model

None

X1

X2

X3

X4

X1 , X2

X1 , X3

X1 , X4

X2 , X3

X2 , X4

X3 , X4

X1 , X2 , X3

X1 , X2 , X4

X1 , X3 , X4

X2 , X3 , X4

X1 , X2 , X3 , X4

R2

C

0.000 1721.6

0.120 1510.8

0.352 1100.1

0.442 939.0

0.527 788.2

0.438 948.7

0.646 580.2

0.528 789.4

0.813 283.7

0.650 573.5

0.687 507.9

0.972

3.0

0.650 574.8

0.719 452.0

0.883 161.7

0.972

5.0

(a) Assume that it is possible to use the C statistic for model building. Use the C statistic,

to determine the best model using forward selection. Justify your selection at

each step.

[8 marks]

(b) Determine the best model overall based on the C statistic. Justify your answer.

[2 marks]

(c) Determine the best model overall based on R2 . Justify your answer.

[2 marks]

2. A regression model is estimated for the dependent variable, y, on x1 and x2 . The following

are all results from this estimation.

Chart A

Chart B

Chart C

Chart D

(a) By testing a suitable hypothesis, determine whether the model is a useful representation of the relationship between the dependent and the independent variables.

Provide evidence for your conclusion.

[3 marks]

(b) How useful would you say that the model is for predicting y?

[2 marks]

(c) Determine which, if any, of the assumptions of a Least Squares Regression are

violated. Justify your answer.

[6 marks]

(d) Do the data appear to be affected by outliers? Justify your answer.

End of Test

Page 2

[3 marks]

X2

1. From some statistical analysis, we have the following table

X in model R” с

None

0.000 1721.6

X

0.120 1510.8

0.352 1100.1

X3

0.442 939.0

X4

0.527 788.2

X1, X2

0.438 948.7

X1, X3

0.646 580.2

X1, X4

0.528 789.4

X₂,

X₃ 0.813 283.7

X₂, X, 0.650 573.5

X3, X,

0.687

507.9

X1, X2, X3 0.972 3.0

X1, X2, X4 0.650 574.8

X1, X3, X4 0.719 452.0

X2, X3, X4 0.883 161.7

X1, X2, X3, X4 0.972 5.0

(a) Assume that it is possible to use the statistic for model building. Use the statistic,

to determine the best model using forward selection. Justify your selection at

each step.

[8 marks)

(b) Determine the best model overall based on the statistic. Justify your answer.

[2 marks]

(c) Determine the best model overall based on R². Justify your answer. [2 marks]

2. A regression model is estimated for the dependent variable, y, on 1 and 19. The following

are all results from this estimation.

. reg y x1 x2

Source

SS

df NS

Number of obs = 15

FC 2 12) = 563.43

Mode! 171754.701 2 85877.3506

Prob F

0.0000

Residual 1829.03208 12 152.41934

R-squared = 0.9895

Adj R-squared = 0.9877

Total 1 173583.733 14 12398.8381

Root MSE

12.346

у |

t

P>It

x

Coef.

6.327888

3.723111

-199.7852

Std. Err.

2037353

1.513925

11.53184

31.06

2.46

-17.32

0.000

0.030

0.000

(95% Conf. Interval]

5.883987 6.771789

4245518 7.02167

-224.911 -174.6595

_cons

1.

1.

HO

Chart A

Chart B

1-

1

Chart C

Chart D

(a) By testing a suitable hypothesis, determine whether the model is a useful repre-

sentation of the relationship between the dependent and the independent variables.

Provide evidence for your conclusion.

[3 marks)

(b) How useful would you say that the model is for predicting y? [2 marks]

(c) Determine which, if any, of the assumptions of a Least Squares Regression are

violated. Justify your answer.

[6 marks)

(d) Do the data appear to be affected by outliers? Justify your answer. [3 marks)

a