Question: 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 upon the day of the week and the weather conditions. The model is of the form:

E(y) = β0 + β1 X1 + β2 X2 + β3 X3 + β4 X1 X3

where: y = daily admissions

X1 = 1 if a weekend, X1 = 0 otherwise

X2 = 1 if sunny, X2 = 0 otherwise

X3 = predicted daily high temperature

After collecting 30 days of data, the following least squares model is obtained:

\(\hat{Y}\) = 105 - 75 X1 + 100 X2 + 10 X3 + 15 X1 X3

with: the standard error of b1 = 10

the standard error of b2 = 30

the standard error of b3 = 4

the standard error of b4 = 3

R2 = 0.96.

a) Interpret the model slope coefficients.

b) Is there sufficient evidence to conclude that attendance increases on sunny days, and, if so, at what significance level?

c) Do the date indicate that the interaction term is useful in this prediction model, if so, at what significance level?

d) Report the estimated regression equation for sunny weekend day at the park