A study in Industrial Marketing Management (February 2016) investigated the impact of service workers' (e.g., waiters and waitresses) personal resources on the quality of the firm's relationship with customers. The study focused on four types of personal resources: flexibility in dealing with customers (x1), service worker reputation (x2), empathy for the customer (x3), and service worker's task alignment (x4). A multiple regression model was employed used to relate these four independent variables to relationship quality (y). Data were collected for n = 220 customers who had recent dealings with a service worker. (All variables were measured on a quantitative scale, based on responses to a questionnaire.)
a. Write a first-order model for E(y) as a function of the four independent variables.
b. Refer to part a. Which b coefficient measures the effect of flexibility (x1) on relationship quality (y), independently of the other independent variables in the model?
c. Repeat part b for reputation (x2), empathy (x3), and task alignment (x4).
d. The researchers theorize that task alignment (x4) "moderates" the effect of each of the other x's on relationship quality (y) - that is, the impact of each x (x1, x2, or x3) on y depends on x4. Write an interaction model for E(y) that matches the researchers' theory.
e. Refer to part d. What null hypothesis would you test to determine if the effect of flexibility (x1) on relationship quality (y) depends on task alignment (x4)?
f. Repeat part e for the effect of reputation (x2) and the effect of empathy (x3).
g. None of the t-tests for interaction were found to be "statistically significant". Given these results, the researchers concluded that their theory was not supported. Do you agree?