Question

In: Statistics and Probability

An office equipment corporation performs preventive maintenance and repair on the line of copiers that it...

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.

Solutions

Expert Solution

Below is the excel output of the regression:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.978517
R Square 0.957495
Adjusted R Square 0.956507
Standard Error 8.913508
Observations 45
ANOVA
df SS MS F Significance F
Regression 1 76960.42 76960.42 968.6572 4.01E-31
Residual 43 3416.377 79.45063
Total 44 80376.8
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -0.5802 2.8039 -0.2069 0.8371 -6.2348 5.0745 -6.2348 5.0745
Serviced 15.0352 0.4831 31.1233 0.0000 14.0610 16.0095 14.0610 16.0095

(c). If the number of copier to be serviced is increased by one then the amount of time of a call increases by 15.0352 minutes on average.

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

Lower 95% Upper 95%
14.0610 16.0095

(e).

Correlation 0.978517
R Square 0.957495

R square is almost 95.75% and this means that the variation in number of copier to be serviced explains around 95.75% of variation in call time.


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