Refer to the data in Table on order fulfillment time.

(a) You decide to develop a regression model using order value, number of products, and location of the retailer as predictors. Find the model equation. Is it significant at α =0.05?

(b) What is R² and interpret its value relative to that in Exercise 1, part (b).

(c) Are all the predictors significant in the presence of others? Use α =0.05.

(d) What can you comment regarding the models for locations A and C?

(e) Interpret the model coefficients of that for location B.

Exercise 1
Refer to the data in Table on order fulfillment time.

(a) You decide to develop a regression model using order value and the number of products in the order as predictors. Find the model equation. Is it significant at α =0.05?

(b) Find R² and R_a²and comment relative to the model in Exercise 2.

(c) Is the predictor, number of products, significant in the presence of the other predictor? Test using α =0.05.

(d) Find a 95% confidence interval for the mean fulfillment time for an order value of $75,000 and number of products being 65.

Exercise 2
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 R_a²? 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).