Question

In: Statistics and Probability

A. Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance...

A. Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars): Weekly Usage (hours) Annual Maintenance Expense ($100) 13 17.0 20 30.0 28 37.0 32 47.0 17 30.5 24 32.5 40 51.5 38 40.0 A2. Using the OLS results and find the predicted value of yi, i.e., , that corresponds with 32 hours of weekly usage of this machine: a. 37.2004 b. 41.2348 c. 33.1660 d. 47.2865 A5. Find sy.x (=sɛ) (standard error of the model): a. 137.4193 b. 4.7857 c. 26.9705 d. 8.9594 A6. Find the 99% confidence interval for β1: a. (0.5555, 1.4617) b. (1.4617, 0.3221) c. (0.3221, 1.6951) d. (0.5555, 1.6951) A7. Using a 5% level of significance, is the effect of “Weekly Usage” on “Annual Maintenance Expense”: a. positively and significantly b. positively and insignificantly c. negatively and significantly d. negatively and insignificantly

Solutions

Expert Solution

Solution: We can use the excel regression data analysis tool to find the answer to the given questions. The excel output is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9120
R Square 0.8318
Adjusted R Square 0.8038
Standard Error 4.7857
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 679.5494948 679.5494948 29.6704924 0.001591769
Residual 6 137.4192552 22.90320921
Total 7 816.96875
Coefficients Standard Error t Stat P-value Lower 99.0% Upper 99.0%
Intercept 8.9594 5.1904 1.7261 0.1351 -10.2837 28.2025
x 1.0086 0.1852 5.4471 0.0016 0.3221 1.6951

Using the OLS results and find the predicted value of yi, i.e., , that corresponds with 32 hours of weekly usage of this machine:

Answer: b. 41.2348

Explanation:

The regression equation is:

Find sy.x (=sɛ) (standard error of the model):

Answer: b. 4.7857

Find the 99% confidence interval for β1:

Answer: c. (0.3221, 1.6951)

Using a 5% level of significance is the effect of “Weekly Usage” on “Annual Maintenance Expense”:

Answer: a. positively and significantly

orchestra answered 2 years ago
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