Refer to given Exercise and the regression model of time to fulfill an order based on order value.
(a) Find a 95% confidence interval for the mean time to fulfill orders that have an order value of $75,000.
(b) Find a 95% prediction interval for the time to fulfill an order for an order of value $75,000. Interpret the difference in the intervals found in parts (a) and (b).
(c) The leverage value for observation 8 is found to be 0.114. Would you consider this observation to have high leverage? Explain.
(d) The studentized residual for observation 17 is found to be 2.840. Using α =0.05, what can you conclude?
(e) The Cook's distance for observation 17is found to be 0.295.What can you conclude?
Exercise
A retail company has information on the time taken (in days) to fulfill an order, the value of the order (in $10,000), the number of different types of products in the order, and the store location. The data are shown in Table.
(a) Find a simple regression model that predicts time to fulfill an order based on value of the order. Interpret the estimated model coefficients.
(b) What is the estimated standard deviation of the error component? Interpret it.
(c) What are the values of R2 and Ra2? Interpret them. a
(d) Is there evidence to conclude that value of the order is a useful predictor? Test using α = 0.01.
(e) Interpret the p-value associated with the test in part (d).