12. A study of 86 savings and loan associations in six northwestern states for 1
ID: 3072646 • Letter: 1
Question
12. A study of 86 savings and loan associations in six northwestern states for 1975 yielded the following cost function: C = 2.38 _ .006 153Q + .000005359Q. 19.2X, (2.84) (2.37) (2.63) (2.69) where C = average operating expense ratio, expressed as a percentage and defined as total operating expense (S million) divided by total assets (S million) times 100 percent Qo output, measured by tdotal assets (S million) X1 ratio of the number of branches to total assets (S 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? Use the probability distribution table for two tailed tests. Don't copy the textbook solution or answers on the internet. They are wrong and not written in clear format!!Explanation / Answer
Solution:
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: Ha: Given regression coefficient or variable is statistically significant.
We assume 5% level of significance or = 0.05.
We are given n = 86, so df = n – 1 = 86 – 1 = 85
Test statistic = t = /SE()
Let us first test for variable Q.
= -0.006153
SE() = 2.37
t = -0.006153/2.37 = -0.002596203
P-value = 0.9951 (by using t-table/excel)
P-value > = 0.05
So, variable Q is not statistically significant.
Now, we have to test for Q2
=0.000005359
SE() = 2.63
t = 0.000005359/2.63 = 0.00000204
P-value = 0.9999 (by using t-table/excel)
P-value > = 0.05
So, variable Q2 is not statistically significant.
For variable X1 test is given as below:
=19.2
SE() = 2.69
t = 19.2/2.69 = 7.137546
P-value = 0.00 (by using t-table/excel)
P-value < = 0.05
So, variable X1 is statistically significant.
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