Lake City has two shops, Zeke\'s and Elmer\'s, that handle the majority of the t

Question

Lake City has two shops, Zeke's and Elmer's, that handle the majority of the town's auto body repairs. Two independent sets of seven cars that were damaged in collisions were taken to these shops for written estimates of the repair costs. These estimates, in dollars, are shown below in table 1. Zeke's Elmer's 1058 995 544 540 1349 1175 1296 1350 605 998 970 1698 1520 676 Table 1: Estimates of repair costs at Zeke's and Elmer's 1. Test the claim that mean repair estimates of all cars at Zeke's and Elmer's are equal using the following sample regression model: C- bo +biZ +e.1 Show all your work step by step and answer the following questions. (a) What do the values of by and bi represent? (b) How does the variance of by compare with variance of difference in sample means for these data? (e) How does the p-value of by compare with p-value of difference in sample means for these data? (d) Compute the F-statistic of the model and compare it to the F-statistic you obtained through the ANOVA exercise for these data.

Explanation / Answer

Here we have to fit regression on Zekes on ELmer's.

There are 7 data points.

We can fit regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : Elmer's--> Predictors : Zeke's--> Results : select second option --> ok --> ok

————— 31-10-2017 15:11:57 ————————————————————

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Regression Analysis: Elmers versus Zekes

The regression equation is
Elmers = 54.9 + 0.889 Zekes

Predictor Coef SE Coef T P
Constant 54.95 94.01 0.58 0.584
Zekes 0.88861 0.08178 10.87 0.000

S = 80.05 R-Sq = 95.9% R-Sq(adj) = 95.1%

Analysis of Variance

Source DF SS MS F P
Regression 1 756601 756601 118.06 0.000
Residual Error 5 32042 6408
Total 6 788643

Intercept b0 = 54.9

Slope b1 = 0.889

Interpretation : For one unit change in Zekes will be 0.889 unit increase in Elmers.

Here we can test two significances :

Overall significance :

Here we have to test the hypothesis that,

H0 : Bj = 0 vs H1 : Bj not= 0

where Bj is the jth population slope

Assume alpha = level of significance = 0.05

Here test statistic follows F-distribution.

Test statistic = 118.06

P-value = 0.000

P-value < alpha

Reject H0 at 5% levelof significance.

Conclusion : Atleast one of the slope is differ than 0.

Individual significance :

Here we have to test the hypothesis that,

H0 : B = 0 vs H1 : B not= 0

where B is the population slope for independent variable.

Assume alpha = level of significance = 0.05

Here test statistic follows t-distribution.

Test statistic = 10.87

P-value = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : The population slope for Zekes is differ than 0.

R-sq = 95.9%

It expresses the proportion of variation in response variable which is explained by variation in independent variable.

We get significance result about F-test and t-test.

By using t-test we can test correlation between independent and dependent variable.

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