Question

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

CC	=	2.38	-	0.006153QQ	+	0.000005359Q2Q2	+	19.2X1X1
											(2.86)		(3.08)		(3.68)		(2.96)

where CC = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent.

QQ = output; measured by total assets ($ million)

X1X1 = ratio of the number of branches to total assets ($ million)

Note: The number in parentheses below each coefficient is its respective t-statistic.

Which of the variable(s) is (are) statistically significant in explaining variations in the average operating expense ratio? (Hint: t0.025,70=1.99t0.025,70=1.99.) Check all that apply.

QQ

X1X1

Q2Q2

What type of average cost-output relationship is suggested by these statistical results?

Cubic

Linear

Quadratic

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?

Economies of scale at lower output levels and diseconomies of scale at higher output levels

Economies of scale at all output levels

Diseconomies of scale at all output levels

Diseconomies of scale at lower output levels and economies of scale at higher output levels

Answer 1

Solution:

Which of the variable(s) is (are) statistically significant in explaining variations in the average operating expense ratio

Here, we have to use t-tests for regression coefficients for testing whether the regression coefficients or variables are statistically significant or not.

Null hypothesis: H₀: Given regression coefficient or variable is not statistically significant.

Alternative hypothesis: H_a: Given regression coefficient or variable is statistically significant.

We assume 5% level of significance or α = 0.05.

We are given n = 86, so df = n – 1 = 86 – 1 = 85

Test statistic = t = β/SE(β)

Let us first test for variable Q.

β = -0.006153

SE(β) = 2.37

t = -0.006153/2.37 = -0.002596203

P-value = 0.9951 (by using t-table/excel)

P-value > α = 0.05

So, variable Q is not statistically significant.

Now, we have to test for Q²

β =0.000005359

SE(β) = 2.63

t = 0.000005359/2.63 = 0.00000204

P-value = 0.9999 (by using t-table/excel)

P-value > α = 0.05

So, variable Q² is not statistically significant.

For variable X₁ test is given as below:

β =19.2

SE(β) = 2.69

t = 19.2/2.69 = 7.137546

P-value = 0.00 (by using t-table/excel)

P-value < α = 0.05

So, variable X₁ is statistically significant.