Question 1
A research has estimated the following multiple regression model for cinema gross box office:
GBO = β0 + β1NOA + β2NFS + β3TPC
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.
(b) Interpret the estimated coefficients for NOA and NFS. Do they make sense or have the sign that you would expect? Explain
(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.
(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?
(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?
|
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
|
Question 2
(a) What is the rationale behind the OLS estimation method?
(b) Explain why the parameters of a Simple Regression model have a sampling distribution. Feel free to use a diagram to help you.
(c) Under what circumstances would we consider using dummy variables, and how would we enter these into our Excel regression?
(d) Under what circumstances would we consider using interaction effects, and how would we enter these into our Excel regression?