Question

7. To determine whether extra personnel are needed for the day, the owners of a water adventure park would like to find a model that would allow them to predict the day’s attendance each morning before opening based on the day of the week and the weather conditions. The model is of the form y = β0 + β1x1 + β2x2 + β3x3 + e where: y = daily admissions, x1 = 1 if weekend, 0 otherwise; x2 = 1 if sunny, 0 if overcast; x3 = predicted daily high temperature (oC) After collecting 30 days of data, the following least squares model was obtained: y = −108 + 190x1 + 210x2 + 42x3 The standard errors of the estimated regression coefficients were s.e.(βˆ 1 = 37), s.e.(βˆ 2 = 43) and s.e.(βˆ 3 = 15). The residual sum of squares was SSE = 1000 and R2 = .585. (a) Is there evidence to conclude that this model is useful in the prediction of daily attendance? (Test H0 : β1 = β2 = β3 = 0 at level .05) (b) Is there evidence to conclude that mean attendance is higher on sunny days than on overcast days, all else being equal? Use a t-test which compares the βˆ 2 to its standard error. Give null and alternative hypotheses, value of test statistic, p-value and conclusion at level .01. (c) All else being held constant, how much does attendance increase on average if the temperature increases 12oC? (d) Use the regression equation to predict the attendance on an overcast Saturday when the temperature is 21 oC. (e) Calculate a 99% confidence interval for β1.

Answer 1