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Forecasting daily admission of a water park. To determine
Chapter 12, Problem 161SE(choose chapter or problem)
Forecasting daily admission of a water park. 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 weather conditions. The model is of the form
\(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}\)
where
\(\begin{array}{l} y=\text { Daily admission } \\ x_{1}=\left\{\begin{array}{ll} 1 & \text { if weekend } \\ 0 & \text { otherwise } \end{array} \quad\right. \text { (dummy variable) } \\ x_{2}=\left\{\begin{array}{ll} 1 & \text { if sunny } \\ 0 & \text { if overcast } \quad \text { (dummy variable) } \end{array}\right. \\ x_{3}=\text { predicted daily high temperature }\left({ }^{\circ} \mathrm{F}\right) \end{array}\)
These data were recorded for a random sample of 30 days, and a regression model was fitted to the data.The least squares analysis produced the following results:
\(\hat{y}=-105+25 x_{1}+100 x_{2}+10 x_{3}\)
with
\(s_{\hat{\beta}_{1}}=10\ \ \ \quad s_{\hat{\beta}_{2}}=30\ \ \ \quad s_{\hat{\beta}_{3}}=4 \quad R^{2}=.65\)
a. Interpret the estimated model coefficients.
b. Is there sufficient evidence to conclude that this model is useful for the prediction of daily attendance?Use \(\alpha\ =\ .05\).
c. Is there sufficient evidence to conclude that the mean attendance increases on weekends? Use \(\alpha\ =\ .10\).
d. Use the model to predict the attendance on a sunny weekday with a predicted high temperature of \(95^{\circ}F\).
e. Suppose the 90% prediction interval for part d is (645,1,245). Interpret this interval.
Questions & Answers
QUESTION:
Forecasting daily admission of a water park. 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 weather conditions. The model is of the form
\(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}\)
where
\(\begin{array}{l} y=\text { Daily admission } \\ x_{1}=\left\{\begin{array}{ll} 1 & \text { if weekend } \\ 0 & \text { otherwise } \end{array} \quad\right. \text { (dummy variable) } \\ x_{2}=\left\{\begin{array}{ll} 1 & \text { if sunny } \\ 0 & \text { if overcast } \quad \text { (dummy variable) } \end{array}\right. \\ x_{3}=\text { predicted daily high temperature }\left({ }^{\circ} \mathrm{F}\right) \end{array}\)
These data were recorded for a random sample of 30 days, and a regression model was fitted to the data.The least squares analysis produced the following results:
\(\hat{y}=-105+25 x_{1}+100 x_{2}+10 x_{3}\)
with
\(s_{\hat{\beta}_{1}}=10\ \ \ \quad s_{\hat{\beta}_{2}}=30\ \ \ \quad s_{\hat{\beta}_{3}}=4 \quad R^{2}=.65\)
a. Interpret the estimated model coefficients.
b. Is there sufficient evidence to conclude that this model is useful for the prediction of daily attendance?Use \(\alpha\ =\ .05\).
c. Is there sufficient evidence to conclude that the mean attendance increases on weekends? Use \(\alpha\ =\ .10\).
d. Use the model to predict the attendance on a sunny weekday with a predicted high temperature of \(95^{\circ}F\).
e. Suppose the 90% prediction interval for part d is (645,1,245). Interpret this interval.
ANSWER:Step 1 of 7
(a)
The model is given below:
where y = Daily admission
The least squares model is given below:
Interpretation:
