Math Question
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he marketing department of California’s Sealand Resorts is the studying the relationship between the number of daily visitors that come to the amusement park, the temperature, and the various media that have been employed. The department decided to vary the number of television commercials shown locally over the 10 consecutive Saturday nights. The data on the number of commercials (Commericals, X1), the high temperature (X2, in degrees), and the number of visitors (Y, Visitors in 1,000’s), is found below.
|
Commercials |
High Temp |
Visitors |
|
2 |
82 |
7.2 |
|
2 |
85 |
7.5 |
|
2 |
83 |
8 |
|
3 |
81 |
10.3 |
|
3 |
79 |
9.4 |
|
3 |
77 |
8.7 |
|
4 |
87 |
12.9 |
|
4 |
86 |
14 |
|
4 |
85 |
14.5 |
|
5 |
78 |
15.4 |
|
5 |
90 |
16.2 |
|
5 |
78 |
14.8 |
|
6 |
88 |
19.9 |
|
6 |
87 |
20 |
|
6 |
88 |
18.9 |
Correlations: Commercials, High Temp, Visitors
Commercials High Temp
High Temp 0.404
0.135
Visitors 0.982 0.520
0.000 0.047
Cell Contents: Pearson correlation
P-Value
Regression Analysis: Visitors Versus Commercials, High Temp
The regression equation is
Visitors = – 11.2 + 2.82 Commercials + 0.156 High Temp.
Predictor Coef SE Coef T P
Constant -11.152 3.486 -3.20 0.008
Commercials 2.8248 0.1261 22.40 0.000
High Temp 0.15590 0.04372 3.57 0.004
S = 0.631707 R-Sq = 98.3% R-Sq(adj) = 98.0%
Analysis of Variance
Source DF SS MS F P
Regression 2 276.28 138.14 346.16 0.000
Residual Error 12 4.79 0.40
Total 14 281.06
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 13.398 0.174 (13.019, 13.778) (11.971, 14.826)
Values of Predictors for New Observations
New Obs Commercials High Temp
1 4.00 85.0
a. Analyze the above output to determine the multiple regression equation.
b. Find and interpret the multiple index of determination (R-Sq).
c. Perform the multiple regression t-tests on 
, 
(use two tailed test with (a = .10). Interpret your results.
d. Predict the number of visitors for a single day where they had four commercials play the night before and the high temperature was 85. Use both a point estimate and the appropriate interval estimate.
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