A study of 86 savings and loan associations in six northwestern states yielded the following cost function:

C = 2. 38 ? 0.006153 Q + 0.000005359 Q2 (squared) + 19.2 X (2.84) ( 2.37) (2.63) (2.69)
where C = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times100 percent
Q = output ; measured by total assets ($million)
X1 = ratio of the number of branches to total assets ($million)
Note: The number in parentheses below each coefficient is its respective t -statistic.
a. Which variable(s) is(are) statistically significant in explaining variations in the average operating expense ratio?

b. What type of cost-output relationship (e.g., linear, quadratic, or cubic) is suggested by these statistical results?

c. Based on these results, what can we conclude about the existence of economies or diseconomies of scale in savings and loan associations in the Northwest?