# Math Question

he marketing department of Californiaâ€™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 1,000â€™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 (= .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.