A researcher analyzes the factors that may influence amusement park attendance.

Question

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = 0 + 1Price + 2Temperature + 3Rides + , where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in °F), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table.

When testing whether the explanatory variables Temperature and Rides are jointly significant, the error sum of squares for the restricted model is SSER = 12,343.78. Which of the following is the value of the test statistic when conducting this test?

df SS MS F Significance F Regression 3 29,524.41 9,841.47 2.18E-14 Residual 26 2,564.37 98.63 Total 29 32,088.78 Coefficients Standard Error t-stat p-value Lower 95% Upper 95% Intercept 27.328 40.254 0.5032 55.415 110.071 Price 1.201 0.294 0.0004 1.805 0.598 Temperature 0.008 0.208 0.9693 0.419 0.435 Rides 3.621 0.364 2.32E-10 2.874 4.369

Explanation / Answer

SSEr for the restricted model = 12343.78

SSReg for the restricted model = TSS - SSEr = 32088.78 - 12343.78 = 19745.

Hence, MSReg = 19745 / 2 = 9872.5

MSEr = 12343.78 / 27 = 457.18

Hence, test statistic for testing the significance of the model = MSReg / MSEr = 9872.5 / 457.18 = 21.59. (Ans).

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