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Q1. An advertising company collected information from 10 Hollywood Movies, including the number of the first...

Q1. An advertising company collected information from 10 Hollywood Movies, including the number of the first year box office reciepts ad the total promotional costs for each movies. They wish to study the relationship between promotion cost and the box office reciepts.

First year box office reciepts (millions) 85.1 106.3 50.2 130.6 54.8 30.3 79.4 91.0 135.4 89.3

Total promotional costs (millions) 5.10 5.80 2.10 8.40 2.90 1.20 3.70 7.60 7.70 4.50

a. If we would like to use the promotion cost to predict the box office reciepts, could you implement a simple regression model? Please use the matrix approach to estimate the reregression coefficients. Report your residual vector e, SSTO, SSR,SSE.

b. check the model assumption of residual assumptions. List all the assumptions made here and use graphs or tests to evaluate at least two of them. Report your R code/ output and your conclusions.

Solutions

Expert Solution

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.929967753
R Square 0.864840021
Adjusted R Square 0.847945023
Standard Error 13.17473061
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 8885.075788 8885.075788 51.18911832 9.66489E-05
Residual 8 1388.588212 173.5735266
Total 9 10273.664
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 23.16330202 9.624829605 2.406619439 0.042733026 0.968405152
promotion cost 12.66871387 1.770694763 7.154657107 9.66489E-05 8.585484426
RESIDUAL OUTPUT
Observation Predicted box office receipt Residuals
1 87.77374277 -2.673742775
2 96.64184249 9.658157514
3 49.76760116 0.432398844
4 129.5804986 1.019501445
5 59.90257225 -5.102572254
6 38.36575867 -8.065758671
7 70.03754335 9.362456647
8 119.4455275 -28.44552746
9 120.7123988 14.68760116
10 80.17251445 9.127485549

milcah answered 1 year ago
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