# Cinema data

a)Excel output:
SUMMARY OUTPUT

Regression Statistics
Multiple R 0.181
R Square 0.033
Standard Error 1.331
Observations 1119

ANOVA
df SS MS F Significance F
Regression 1 67.399 67.399 38.043 0.000
Residual 1117 1978.968 1.772
Total 1118 2046.367

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 9.763 0.858 11.376 0.000 8.079 11.446
ln(P) -2.040 0.331 -6.168 0.000 -2.689 -1.391

1. The elasticity of demand estimated is the absolute value of the coefficient of ln(P) which is equal to 2.040.
2. The 95% confidence interval for the elasticity is [1.391,2.689]. Interpretation: At 5% level of significance, we can conclude that the elasticity of demand lies in the interval [1.391, 2.689].
b)Excel output:
SUMMARY OUTPUT

Regression Statistics
Multiple R 0.569
R Square 0.324
Standard Error 189.792
Observations 1119

ANOVA
df SS MS F Significance F
Regression 6 19188251.659 3198042 88.783 0.000
Residual 1112 40055229.775 36020.890
Total 1118 59243481.433

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -190.336 169.282 -1.124 0.261 -522.484 141.812
PRICE -38.024 3.961 -9.598 0.000 -45.797 -30.251
BUDGET 121.027 20.224 5.984 0.000 81.345 160.709
WEEK -41.856 2.307 -18.142 0.000 -46.383 -37.329
SEQUEL 126.918 27.870 4.554 0.000 72.233 181.602
REVIEW 31.731 8.644 3.671 0.000 14.771 48.691
STAR 72.828 14.334 5.081 0.000 44.703 100.953

1. R2 = 0.324
2. Test H0:ß1 = ß2 =… = ß6 = 0

HA: At lease one ßi ? 0
Decision: Since F = 88.783 >Fcrit = F6,1112,0.01 =0.145, H0 is rejected at 1% level of significance.
Conclusion: At 1% level of significance, H0 is rejected, so at least one ßi ? 0.
3. PRICE: 1 unit increase in price will lead to 38.024 units decrease in attendance.
BUDGET: 1 unit increase in budget will lead to 121.027 units increase in attendance.
WEEK: 1 week later of release will lead to 41.856 units decrease in attendance.
SEQUEL: Movies that have a sequel will have 126.918 units of attendance more than movies which don’t have a sequel.
REVIEW: 1 unit increase critical review score will lead to 31.731 units increase in attendance.
STAR: Movies with lead actors will have 72.828 units of attendance more than those without lead actors.
c) Excel output:
SUMMARY OUTPUT

Regression Statistics
Multiple R 0.568
R Square 0.323
Standard Error 190.209
Observations 1119

ANOVA
df SS MS F Significance F
Regression 9 19120352.159 2124483.573 58.721 0.000
Residual 1109 40123129.274 36179.558
Total 1118 59243481.433

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 767.806 62.539 12.277 0.000 645.099 890.514
PRICE -43.995 4.246 -10.363 0.000 -52.325 -35.665
BUDGET 0.000 0.000 4.086 0.000 0.000 0.000
WEEK -40.929 2.306 -17.750 0.000 -45.453 -36.405
SEQUEL 133.183 29.866 4.459 0.000 74.583 191.782
REVIEW 23.315 8.434 2.765 0.006 6.767 39.862
STAR 90.085 14.054 6.410 0.000 62.509 117.661
FRI 42.086 17.476 2.408 0.016 7.797 76.375
SAT 66.857 17.434 3.835 0.000 32.650 101.063
SUN 33.344 17.519 1.903 0.057 -1.031 67.719

1.Since the P-values of the three new dummy variables FRI, SAT and SUN are
PFRI = 0.016 > 0.01, PSAT = 0.000 < 0.01, PSUN = 0.057 > 0.01
only dummy variable SAT is significant at 1% level of significance.
2. The coefficients’ signs are all positive, and this supports our intuition of increased attendance on weekends.
3. Variable SAT has the largest coefficient compared to the other dummy variables, so Saturday appears to have the greatest affect on attendance.
d)Excel output:
SUMMARY OUTPUT

Regression Statistics
Multiple R 0.612
R Square 0.374
Standard Error 183.105
Observations 1119

ANOVA
df SS MS F Significance F
Regression 12 22162238.667 1846853.222 55.085 0.000
Residual 1106 37081242.766 33527.344
Total 1118 59243481.433

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 827.734 60.552 13.670 0.000 708.924 946.544
PRICE -46.824 4.123 -11.356 0.000 -54.914 -38.733
BUDGET 0.000 0.000 1.618 0.106 0.000 0.000
WEEK -33.191 2.368 -14.016 0.000 -37.837 -28.544
SEQUEL 158.412 29.033 5.456 0.000 101.446 215.378
REVIEW 0.308 8.585 0.036 0.971 -16.536 17.152
STAR 96.163 13.547 7.098 0.000 69.582 122.744
OPENINGDAY 146.065 37.688 3.876 0.000 72.117 220.014
PUBLIC 52.443 35.406 1.481 0.139 -17.027 121.912
SCHOOL 103.857 12.897 8.053 0.000 78.552 129.162
FRI 38.039 17.321 2.196 0.028 4.053 72.025
SAT 69.143 16.958 4.077 0.000 35.870 102.417
SUN 36.203 17.037 2.125 0.034 2.774 69.631

Since the P-values of dummy variables OPENINGDAY, PUBLIC and SCHOOL are
POPENINGDAY = 0.000 < 0.01, PPUBLIC = 0.139 > 0.01, PSCHOOL = 0.000 < 0.01,
variables OPENINGDAY and SCHOOL are significant at 1% level of significance.
And since the coefficients of these three variables are all positive, this confirms the intuition of higher attendance on opening days, public holidays and in school holiday periods.
e)Excel output:
SUMMARY OUTPUT

Regression Statistics
Multiple R 0.616
R Square 0.379
Standard Error 182.486
Observations 1119

ANOVA
df SS MS F Significance F
Regression 14 22479006.222 1605643.302 48.216 0.000
Residual 1104 36764475.211 33301.155
Total 1118 59243481.433

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 836.519 61.510 13.600 0.000 715.829 957.209
PRICE -47.331 4.143 -11.425 0.000 -55.460 -39.203
BUDGET 0.000 0.000 1.565 0.118 0.000 0.000
WEEK -32.919 2.362 -13.938 0.000 -37.553 -28.284
SEQUEL 158.649 28.966 5.477 0.000 101.815 215.484
REVIEW -0.918 8.568 -0.107 0.915 -17.730 15.893
STAR 96.322 13.503 7.133 0.000 69.828 122.817
MAXTOAVDIFF -7.750 2.516 -3.081 0.002 -12.686 -2.814
RAINFALL -0.087 0.756 -0.115 0.908 -1.570 1.396
OPENINGDAY 146.672 37.612 3.900 0.000 72.873 220.471
PUBLIC 43.592 35.451 1.230 0.219 -25.966 113.151
SCHOOL 107.128 12.963 8.264 0.000 81.694 132.563
FRI 45.215 17.578 2.572 0.010 10.724 79.705
SAT 84.632 17.833 4.746 0.000 49.642 119.623
SUN 46.852 17.573 2.666 0.008 12.371 81.333

Test H0: ßMAX = ßRAIN = 0
HA: At least one of ßMAX or ßRAIN is non-zero
Compared to the excel output in d), test statistic is
F = (SSRF – SSRR)/(k-p)SSEF/(n-k-1) =(22479006.222 – 22162238.667)/(14-2)36764475.211/(1119-14-1)= 0.793
Under H0, F ~ Fk-p, n-k-1, a
Decision: Since F < F12, 1104, 0.05 = 1.761, do not reject H0 at 5% level of significance.
Conclusion: At 5% level of significance, do not reject H0so ßMAX = ßRAIN = 0, and we can conclude that the model in e) (full model) can be reduced to the model in d) (reduced model) i.e. the two additional variables MAXTOAVDIFF and RAINFALL should not be included in the model.
f)Use the excel output in question d)

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.612
R Square 0.374
Standard Error 183.105
Observations 1119

ANOVA
df SS MS F Significance F
Regression 12 22162238.667 1846853.222 55.085 0.000
Residual 1106 37081242.766 33527.344
Total 1118 59243481.433

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 827.734 60.552 13.670 0.000 708.924 946.544
PRICE -46.824 4.123 -11.356 0.000 -54.914 -38.733
BUDGET 0.000 0.000 1.618 0.106 0.000 0.000
WEEK -33.191 2.368 -14.016 0.000 -37.837 -28.544
SEQUEL 158.412 29.033 5.456 0.000 101.446 215.378
REVIEW 0.308 8.585 0.036 0.971 -16.536 17.152
STAR 96.163 13.547 7.098 0.000 69.582 122.744
OPENINGDAY 146.065 37.688 3.876 0.000 72.117 220.014
PUBLIC 52.443 35.406 1.481 0.139 -17.027 121.912
SCHOOL 103.857 12.897 8.053 0.000 78.552 129.162
FRI 38.039 17.321 2.196 0.028 4.053 72.025
SAT 69.143 16.958 4.077 0.000 35.870 102.417
SUN 36.203 17.037 2.125 0.034 2.774 69.631

Since the P-values of variables BUDGET, REVIEW, PUBLIC, FRI, SUN are greater than 0.01, these variables are insignificant at the 1% level of significance. So we reduce the model and get a new excel output:
SUMMARY OUTPUT

Regression Statistics
Multiple R 0.605464052
R Square 0.366586718
Standard Error 183.784
Observations 1119

ANOVA
df SS MS F Significance F
Regression 7 21717873.412 3102553.345 91.856 0.000
Residual 1111 37525608.022 33776.425
Total 1118 59243481.433

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 794.446 53.224 14.926 0.000 690.015 898.878
PRICE -42.702 3.905 -10.936 0.000 -50.363 -35.040
WEEK -32.840 2.102 -15.625 0.000 -36.963 -28.716
SEQUEL 182.031 24.308 7.489 0.000 134.336 229.726
STAR 106.417 11.820 9.003 0.000 83.226 129.609
OPENINGDAY 126.149 37.347 3.378 0.001 52.872 199.427
SCHOOL 114.053 11.642 9.796 0.000 91.209 136.896
SAT 51.397 16.059 3.200 0.001 19.887 82.907

The regression model for admission is:
ADMISSION = -42.702*PRICE – 32.840*WEEK + 182.031*SEQUEL + 106.417*STAR + 126.149*OPENINGDAY + 114.053*SCHOOL + 51.387*SAT + 794.446
According to the information given by the boss, PRICE = 12, WEEK = 3, SEQUEL = 1, STAR = 1, OPENINGDAY = 0, SCHOOL = 0, SAT = 1.
Plug in the model and we can get ADMISSION = 523 (rounded to integer)
g)

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