The exercise involving data in this and subsequent sections were designed to be
ID: 3156393 • Letter: T
Question
The exercise involving data in this and subsequent sections were designed to be solved using Excel. The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.
The data set is available in file named Showtime. All data sets can be found in your eBook or on your Student CD. Click on the webfile logo to reference the data. a. Use = .01 to test the hypotheses for the model y = 0 + 1x1 + 2x2 + , where Compute the F test statistic (to 4 decimals). What is the p-value? What is your conclusion? b. Use = .05 to test the significance of 1. Compute the t test statistic (to 4 decimals). What is the p-value? What is your conclusion? Should x1 be dropped from the model? c. Use = .05 to test the significance of 2. Compute the t test statistic (to 4 decimals). What is the p-value? What is your conclusion? Should x2 be dropped from the model?
Explanation / Answer
The data set is available in file named Showtime. All data sets can be found in your eBook or on your Student CD. Click on the webfile logo to reference the data.
The regression line is y =83.2301+2.2902*x1+1.3010*x2
Calculated F=28.3778, P=0.0019 < 0.01 level of significance.
The model is significant.
b. Use = .05 to test the significance of 1. Compute the t test statistic (to 4 decimals). What is the p-value? What is your conclusion? Should x1 be dropped from the model?
t=2.2902/0.3041 =7.532 P=0.0007 < 0.05 level of significance.
X1 is significantly predicting y. x1 should not be dropped from the model.
c. Use = .05 to test the significance of 2. Compute the t test statistic (to 4 decimals). What is the p-value? What is your conclusion? Should x2 be dropped from the model?
t=1.3010/0.3207 =4.057 P=0.0098 < 0.05 level of significance.
X2 is significantly predicting y. x2 should not be dropped from the model.
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
28.3778
.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
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
28.3778
.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
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