Increasing customer satisfaction typically results in increased purchase behavior. For many products, there is more than one measure of customer satisfaction. In many of these instances, purchase behavior can increase dramatically with an increase in any one of the customer satisfaction measures, not necessarily all of them at the same time. Gunst and Barry ("One Way to Moderate Ceiling Effects," Quality Progress, October 2003, pp. 83-85) consider a product with two satisfaction measures, $X_1$ and $X_2$, that range from the lowest level of satisfaction, 1 , to the highest level of satisfaction, 7. The dependent variable, $Y$, is a measure of purchase behavior, with the
highest value generating the most sales. The following regression equation is presented:
$$
\hat{Y}_i=-3.888+1.449 X_{1 i}+1.462 X_{2 i}-0.190 X_{1 i} X_{2 i}
$$
Suppose that $X_1$ is the perceived quality of the product and $X_2$ is the perceived value of the product. (Note: If the customer thinks the product is overpriced, he or she perceives it to be of low value and vice versa.)
a. What is the predicted purchase behavior when $X_1=2$ and $X_2=2$ ?
b. What is the predicted purchase behavior when $X_1=2$ and $X_2=7$ ?
c. What is the predicted purchase behavior when $X_1=7$ and $X_2=2$ ?
d. What is the predicted purchase behavior when $X_1=7$ and $X_2=7$ ?
e. What is the regression equation when $X_2=2$ ? What is the slope for $X_1$ now?
f. What is the regression equation when $X_2=7$ ? What is the slope for $X_1$ now?
g. What is the regression equation when $X_1=2$ ? What is the slope for $X_2$ now?
h. What is the regression equation when $X_1=7$ ? What is the slope for $X_2$ now?
i. Discuss the implications of (a) through (h) within the context of increasing sales for this product with two customer satisfaction measures.