Management of a soft-drink bottling company has the business objective of developing a method for allocating delivery costs to customers. Although one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases of soft drink at the delivery point. To begin, management decided to develop a regression model to predict delivery time based on the number of cases delivered. A sample of 20 deliveries within a territory was selected. The delivery times and the number of cases delivered were organized in the following table (and stored in Delivery):
$$
\begin{array}{|c|c|c|c|c|c|}
\hline \text { Customer } & \begin{array}{c}
\text { Number } \\
\text { of } \\
\text { Cases }
\end{array} & \begin{array}{c}
\text { Delivery } \\
\text { Time } \\
\text { (Minutes) }
\end{array} & \text { Customer } & \begin{array}{c}
\text { Number } \\
\text { of } \\
\text { Cases }
\end{array} & \begin{array}{l}
\text { Delivery } \\
\text { Time } \\
\text { (Minutes) }
\end{array} \\
\hline 1 & 52 & 32.1 & 11 & 161 & 43.0 \\
\hline 2 & 64 & 34.8 & 12 & 184 & 49.4 \\
\hline 3 & 73 & 36.2 & 13 & 202 & 57.2 \\
\hline 4 & 85 & 37.8 & 14 & 218 & 56.8 \\
\hline 5 & 95 & 37.8 & 15 & 243 & 60.6 \\
\hline 6 & 103 & 39.7 & 16 & 254 & 61.2 \\
\hline 7 & 116 & 38.5 & 17 & 267 & 58.2 \\
\hline 8 & 121 & 41.9 & 18 & 275 & 63.1 \\
\hline 9 & 143 & 44.2 & 19 & 287 & 65.6 \\
\hline 10 & 157 & 47.1 & 20 & 298 & 67.3 \\
\hline
\end{array}
$$
a. Use the least-squares method to compute the regression coefficients $b_0$ and $b_1$.
b. Interpret the meaning of $b_0$ and $b_1$ in this problem.
c. Predict the delivery time for 150 cases of soft drink.
d. Should you use the model to predict the delivery time for a customer who is receiving 500 cases of soft drink? Why or why not?
e. Determine the coefficient of determination, $r^2$, and explain its meaning in this problem.
f. Perform a residual analysis. Is there any evidence of a pattern in the residuals? Explain.
g. At the 0.05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases delivered?
h. Construct a $95 \%$ confidence interval estimate of the mean delivery time for 150 cases of soft drink and a $95 \%$ prediction interval of the delivery time for a single delivery of 150 cases of soft drink.