Question

An office equipment corporation performs preventive maintenance and repair on the line of copiers that it sells. For 45 recent service calls data has been collected on the number of copiers serviced during the call and the number of minutes spent on the call by the service person. The company would like to develop a regression model that can be used to predict the amount of time (in minutes) that a call will require based on the number of copiers that need to be serviced.

Minutes	Serviced
20	2
60	4
46	3
41	2
12	1
137	10
68	5
89	5
4	1
32	2
144	9
156	10
93	6
36	3
72	4
100	8
105	7
131	8
127	10
57	4
66	5
101	7
109	7
74	5
134	9
112	7
18	2
73	5
111	7
96	6
123	8
90	5
20	2
28	2
3	1
57	4
86	5
132	9
112	7
27	1
131	9
34	2
27	2
61	4
77	5

(c)        Interpret the value of the sample slope in the context of this problem.

(d)          Find a 95% confidence interval for the population slope.

(e)          Report and interpret the value of the coefficient of determination R². Also calculate the value of the correlation coefficient r.

Answer 1

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R Console >xc (2,4,3, 2,1,10,S, 5, 1,2,9, 10, 6, 3, 4,8,7,8, 10,4,5,7,7,5,9, 7,2,5,7, 6, 8,5,2,2,1, y-c ( 20 , 60, 46, 41, 12, 137, 68,89, 4, 32, 144, l156, 93, 36, 72,100, 105, 131, 127, 57, 66, 101, > summary (1m (y-x)) Untitled- REditor Call: x-c (2,4,3,2,1,10,5,5,1,2,9, 10, 6, 3, 4, 8,7,8,10,4,5,7,7,S, y-c (20,60,46,41,12,137,68,89,4,32,144,156,93,36,72,100, summary (1m (y-x)) t-qt (0.975,43) u-15.0352+(t*0.4831) 1-15.0352-(t*0.4831) 1m (formula y x) Residuals: Min 10 Median 3Q Max -22.7723 -3.7371 0.3334 6.3334 15.4039 Coefficients 1 Estimate Std. Error t value Pr (>It) cor (x, y) (Intercept) -0.5802 2.8039 -0.207 0.837 15.0352 0.4831 <2e-16 * 31.123 ' 1 Signif. codes: O 0.001 0.01 0.05.0.1 Residual standard error: 8.914 on 43 degrees of freedom Multiple R-squared: o.9575, F-statistic: Adjusted R-squared: p-value: <2.2e-16 0.9565 968.7 on 1 and 43 DF, tqt (0.975, 43) u-15.0352+(t 0.4831) 1-15.0352-(0.4831) [116.00946 1 [1] 14.06094 Cor (x, y) [1] 0.978517