Part 3 please Itiple Regression Problem (Chapters. 15) The manager of Showtime M
ID: 3315637 • Letter: P
Question
Part 3 please Itiple Regression Problem (Chapters. 15) The manager of Showtime Movie Theaters Inc, Boardman, would like to estimate the effects of advertising expenditures on weekly do the analysis for her. The following historical data for a sample of eight weeks are given to you gross revenue using regression analysis. The manager hires you to Weekly Gross Weekly ITV Advertising Weekly ($1000s) 5.0 2.0 4.0 ($1000s) 1.5 2.0 Revenue ($1000s) 96 90 95 92 95 94 94 94 2.5 3.3 3.5 2.5 4.2 2.5 Note: Please attach Excel output with complete results. la. Explain to the managers the causal relationship between Weekly Gross Sales, TV Advertising and X2, respectively). b. Formulate a multiple LRM that relates Y to X and X per Advertising. In your statement identify the DV (call it Y) and the IVs (call them X and e. What are your expected signs of the regression parameters? 2a. Use Excel to estimate the model that you have specified in part 1b above. b. Are the estimated signs consistent with you expectation on the basis of theory? Please be specific. 3. Use the results in your Excel output to answer these questions a. Interpret the coefficient of determination estimate in the context of this problem b. Interpret the meaning of the estimates for 'a·h, and C. Is the multiple LRM you formulated in part lb statistically significant? Verify at 5% level of significance. d. Suppose the owner plans to spend $3000 a week on TV advertising and $1800 a week on newspaper advertising, how much should the owner expect to gross in revenue for a week ( thesimpurvgression medels and) using the multiple regression model? e. Which medium of advertising is relatively more important in predicting gross revenue and why?
Explanation / Answer
Result:
a).. R square =0.919
91.9% of variance in gross revenue is explained by the model.
b).
when both TV advertising and newspaper advertising are 0, the expected gross revenue is $83230.
when TV advertising increases by $1000, the expected gross revenue increases by $2290.
when newpaper advertising increases by $1000, the expected gross revenue increases by $1301.
c).
calculated F=28.38, P=0.0019 which is < 0.05 level.
The model is significant.
d).
predicted weekly gross sales =$92442
e).
comparing the coefficients, TV advertising is relatively more important in prediction.
Regression Analysis
R²
0.919
Adjusted R²
0.887
n
8
R
0.959
k
2
Std. Error
0.643
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
23.4354
2
11.7177
28.38
.0019
Residual
2.0646
5
0.4129
Total
25.5000
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=5)
p-value
95% lower
95% upper
Intercept
83.2301
1.5739
52.882
4.57E-08
79.1843
87.2759
x1
2.2902
0.3041
7.532
.0007
1.5086
3.0718
x2
1.3010
0.3207
4.057
.0098
0.4766
2.1254
Predicted values for: y
95% Confidence Interval
95% Prediction Interval
x1
x2
Predicted
lower
upper
lower
upper
Leverage
3
1.8
92.442
91.569
93.316
90.574
94.311
0.280
Regression Analysis
R²
0.919
Adjusted R²
0.887
n
8
R
0.959
k
2
Std. Error
0.643
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
23.4354
2
11.7177
28.38
.0019
Residual
2.0646
5
0.4129
Total
25.5000
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=5)
p-value
95% lower
95% upper
Intercept
83.2301
1.5739
52.882
4.57E-08
79.1843
87.2759
x1
2.2902
0.3041
7.532
.0007
1.5086
3.0718
x2
1.3010
0.3207
4.057
.0098
0.4766
2.1254
Predicted values for: y
95% Confidence Interval
95% Prediction Interval
x1
x2
Predicted
lower
upper
lower
upper
Leverage
3
1.8
92.442
91.569
93.316
90.574
94.311
0.280
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