4. A computer repair service is examining the time taken on service calls. The d

Question

4. A computer repair service is examining the time taken on service calls. The data obtained for 30 service calls are listed below. Information obtained includes:

Number of machines to be repaired (NUMBER)

Years of experience of service person (EXPER)

Time taken (in minutes) to provide service (TIME)

EXPER and NUMBER are explanatory variables.

(a) What’s the estimated regression equation?

(b) Is there any insignificant factor?

(c) What percentage of the variation in y has been explained by the regression?

(d) If the service person has 5-year experience and the number of machines to be repaired is 10. Predict the time to provide service.

NUMBER EXPER TIME 1 9 66 1 11 74 3 11 88 4 8 99 6 9 134 6 9 120 7 10 178 8 9 139 9 8 187 11 10 227 11 10 225 12 7 270 13 9 265 14 9 301 15 10 343 16 11 383 17 10 383 20 9 515 19 9 474 20 9 495 22 9 628 22 9 636 23 10 660 24 10 731 25 11 752 26 8 800 27 10 863 28 9 918 29 9 976 30 10 1027

Explanation / Answer

Here i am providing excel output for the given multiple regression.

(a) Here the estimated regression equation is

TIME = -179.288 + 32.9688 * NUMBER + 10.1889 * EXPER

(b) As the p - value for the variable EXPER is greater than the significance level 0.05 so we caan say this factor is insignificanct here.

(c) Here EXPER = 5

NUMBER = 10

TIME = -179.288 + 32.9688 * NUMBER + 10.1889 * EXPER

= -179.288 + 32.9688 * 10 + 10.1889 * 5  

= 201.3445

(d) Here we will explain it by the value of R2 . Here as R2 = 0.9514

that means 95.14% variationn in y is explained by the variation the both independent variables. Rest are from environment factors.

SUMMARY OUTPUT Regression Statistics Multiple R 0.975402 R Square 0.951408 Adjusted R Square 0.947809 Standard Error 68.41184 Observations 30 ANOVA df SS MS F Significance F Regression 2 2474190 1237095 264.3263 1.86E-18 Residual 27 126364.9 4680.18 Total 29 2600555 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -179.288 125.5799 -1.42768 0.164849 -436.956 78.38083 -436.956 78.38083 NUMBER 32.96881 1.4358 22.96198 2.99E-19 30.02279 35.91483 30.02279 35.91483 EXPER 10.18887 13.11943 0.776624 0.444131 -16.73 37.10771 -16.73 37.10771

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