vANSWER ALL QUESTIONS: 50 MARKS IN TOTAL
vANSWER 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  4.27E13  
Residual  17  39275.93  2310.349  
Total  20  1293290  
Coefficien  Standard  t Stat  Pvalue  Lower  Upper  
ts  Error  95%  95%  
Intercept  279.29 108.9081 2.56445 0.020103 509.066 49.5137  
NOA  8.673796  1.174789  7.383281  1.07E06  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 onesided 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)
Page 1 of 3
(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 Fstatistic and corresponding pvalue testing in the above regression? Sketch (roughly) the F distribution, and indicate the relative locations of the Fstat, Fcrit (which is, in this case, 3.01), and the rejection region for an Ftest 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  1.68E19  
Residual  16  4424.853  276.5533  
Total  20  1293290  
Coefficient  Standard  t Stat  Pvalue  Lower  Upper  
s  Error  95%  95%  
Intercept  26.01854  46.46992  0.559901  0.583302  72.4933  124.5304  
No. of admissions (millions)  8.10597 1.549022 5.23296 8.21E05 11.3898 4.82219  
No. of admissions (millions)^2  0.124897  0.011126  11.22584  5.37E09 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  5.49E07  27.96679  48.11051  
Page 2 of 3
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 ****

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Solution: vANSWER ALL QUESTIONS: 50 MARKS IN TOTAL