Econometrics Practice Final Exam

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ANSWER ALL QUESTIONS: 50 MARKS IN TOTAL

Econometrics Practice Final Exam

Question 1 (30 MARKS)

A research has estimated the following multiple regression model for cinema gross box office:

GBO =

Where GBO is the gross box office, NOA is the number of admissions, NFS is the number of films

screened and TPC is the top price of cinema ticket.

An (incomplete) regression output is shown as follow:

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.984698

R Square 0.969631

Adjusted R Square 0.964272

Standard Error 48.06609

Observations 21

ANOVA

df SS MS F Significance F

Regression 3 1254015 418004.9 180.9272 4.27E-13

Residual 17 39275.93 2310.349

Total 20 1293290

Coefficien ts

Standard Error

t Stat P-value Lower 95%

Upper 95%

Intercept -279.29 108.9081 -2.56445 0.020103 -509.066 -49.5137

NOA 8.673796 1.174789 7.383281 1.07E-06 6.195208 11.15238

NFS -0.10242 0.515111

TPC 21.59475 13.0633 1.653085 0.11666 -5.96641 49.1559

(a) Perform a one-sided significance test for the coefficient for NFS. Use a 5% significance level. It might be useful to note that “=T.INV.2T(0.05,17)” = 2.11, “=T.INV.2T(0.5,17)” = 0.69 and “=T.INV.2T(0.1,17)” = 1.74.

(5 Marks)

(b) Interpret the estimated coefficients for NOA and NFS. Do they make sense or have the sign that you would expect? Explain

(5 Marks)

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(c) Construct a 95% confidence interval for NFS. Interpret this interval. Once again, it might be useful to note that “=T.INV.2T(0.05,17)” = 2.11,

“=T.INV.2T(0.5,17)” = 0.69 and “=T.INV.2T(0.1,17)” = 1.74.

(5 Marks)

(d) What are the F-statistic and corresponding p-value testing in the above regression? Sketch (roughly) the F distribution, and indicate the relative locations of the F-stat, F-crit (which is, in this case, 3.01), and the rejection region for an F-test on this model. What would your conclusion be?

(5 Marks)

(e) The researcher has also estimated a quadratic relationship between the number of admissions and the gross box office. Where the regression output is shown as follow. What are the major differences you have found from the previous model? Can you think of any reasons to these differences?

(10 Marks)

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.998288

R Square 0.996579

Adjusted R Square 0.995723

Standard Error 16.62989

Observations 21

ANOVA

df SS MS F Significance F

Regression 4 1288866 322216.4 1165.115 1.68E-19

Residual 16 4424.853 276.5533

Total 20 1293290

Coefficient s

Standard Error

t Stat P-value Lower 95%

Upper 95%

Intercept 26.01854 46.46992 0.559901 0.583302 -72.4933 124.5304

No. of admissions (millions) -8.10597 1.549022 -5.23296 8.21E-05 -11.3898 -4.82219

No. of admissions (millions)^2 0.124897 0.011126 11.22584 5.37E-09 0.101311 0.148483

No of films screened -0.10448 0.178218 -0.58626 0.56588 -0.48229 0.273323

Top price of cinema ticket ($) 38.03865 4.751088 8.006303 5.49E-07 27.96679 48.11051

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Question 2 (20 MARKS)

(a) What is the rationale behind the OLS estimation method? (5 Marks)

(b) Explain why the parameters of a Simple Regression model have a sampling distribution. Feel free to use a diagram to help you.

(5 Marks)

(c) Under what circumstances would we consider using dummy variables, and how would we enter these into our Excel regression?

(5 Marks)

(d) Under what circumstances would we consider using interaction effects, and how would we enter these into our Excel regression?

(5 Marks)

**** End of Examination ****