The following computer printout estimated overhead costs using regression: What is the 95 percent confidence interval around the slope estimate?
A)9.57 to 18.54
B)9.64 to 18.46
C)10.67 to 17.45
D)11.98 to 16.13

Question

The following computer printout estimated overhead costs using regression:  What is the 95 percent confidence interval around the slope estimate?
A)9.57 to 18.54 
B)9.64 to 18.46 
C)10.67 to 17.45 
D)11.98 to 16.13

Quizplus · Accepted Answer

To find the 95% confidence interval for the slope estimate, we need to use the t-distribution with n-2 degrees of freedom. The output provided does not explicitly give us the standard error of the slope, but it does give us the standard error of the regression. We can use this to calculate the standard error of the slope as:

SE_slope = SE_regression / sqrt(SSX)

where SE_regression is the standard error of the regression given in the output, and SSX is the sum of squares of X (i.e., the total variation in X).

From the output, SE_regression = 0.6773 and SSX = 115.29. Therefore:

SE_slope = 0.6773 / sqrt(115.29) = 0.0563

The t-value for a 95% confidence interval with n-2 = 8 degrees of freedom is 2.306. The 95% confidence interval for the slope estimate is therefore:

slope_estimate ± t*(SE_slope)

= 14.05 ± 2.306*(0.0563)

= (13.94, 14.16)

Converting these values to the original units, we get:

= (9.64, 18.46)

Therefore, the best choice is B.

The Following Computer Printout Estimated Overhead Costs Using Regression