Question

In: Math

Customer Months Since Last Service (x1) Type of Repair Electrical (0) Mechanical (1) (x2) Truck (1)...

Customer

Months Since
Last Service (x1)

Type of Repair

Electrical (0)

Mechanical (1)

(x2)

Truck (1)
or
Car (0)

(x3)

Mileage of Vehicle

(x4)

Repair Time
in hours (y)

1

2

1

1

98855

2.9

2

6

0

0

86883

3

3

8

1

1

75645

4.8

4

3

0

0

97823

1.8

5

2

1

1

62099

2.9

6

7

1

0

67697

4.9

7

9

0

1

73113

4.2

8

8

0

0

76240

4.8

9

4

1

1

71170

4.4

10

6

1

1

60626

4.5

An analyst at a local automotive garage wanted to see if there were relationships between repair time in hours (y) and months since last service(x1), type of repair(x2), whether it was a truck or car(x3), or the mileage of the vehicle(x4). Use a level of significance of 0.05.

  1. What is the dependent variable?

  1. What are the independent variables?

  1. Run the regression analysis with the four independent variables. Write out the prediction equation.
  1. From a global perspective is the model worth keeping? Why?

  1. Evaluate the individual independent variables, circle the variables would you consider removing? Explain why?          X1                         X2                           X3                            X4

  1. Rerun the regression analysis after removing the unnecessary independent variables. Write the regression equation:
  1. What repair time will it take for a car with 90000 miles, not serviced for six months, and requires for electrical repairs?

Solutions

Expert Solution

1:

The dependent variable is:

Repair times in hour

-----------------------------

2:

The independent variables:

Months Since Last Service,

Type of Repair Electrical (0) Mechanical (1),

Truck (1) or Car (0),

Mileage of Vehicle

-------------------------

3:

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.936550158
R Square 0.877126198
Adjusted R Square 0.778827156
Standard Error 0.507390569
Observations 10
ANOVA
df SS MS F Significance F
Regression 4 9.18877405 2.297193512 8.923039162 0.016897485
Residual 5 1.28722595 0.25744519
Total 9 10.476
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 2.284192218 1.764451241 1.294562391 0.252029574 -2.251474091 6.819858526
X1 0.353129727 0.082490263 4.280865589 0.007857034 0.141081756 0.565177697
X2 1.164299608 0.478798629 2.431710406 0.059255638 -0.06649145 2.395090667
X3 -0.171488843 0.406240421 -0.422136338 0.690462098 -1.215763089 0.872785402
X4 -1.30116E-05 1.6542E-05 -0.786581632 0.467152578 -5.55342E-05 2.95109E-05

The prediction equation is

y' = 2.2842 +0.3531*x1+1.1643*x2-0.1715*x3-0.000013*X4

----------------

4:

The p-value of F is 0.0169

Since p-value is less than 0.05 so model is significant at 5% level of significance.

--------------------

5:

The p-value of all variable except X1 is greater than 0.05 so only this variable is significant to the model.

-----------------

6:

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.730873795
R Square 0.534176504
Adjusted R Square 0.475948567
Standard Error 0.781022322
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 5.596033058 5.596033058 9.17388683 0.016338159
Residual 8 4.879966942 0.609995868
Total 9 10.476
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 2.147272727 0.604977289 3.549344356 0.007516627 0.752192597 3.542352857
X1 0.304132231 0.100412033 3.02884249 0.016338159 0.072581669 0.535682794

The regression equation is:

y'=2.1473 +0.3041*X1

-----------------

7:

Here we have

X1=6, X2=0, X3=0, X4 = 90000

The required predicted value is:

y' = 2.2842 +0.3531*6+1.1643*0-0.1715*0-0.000013*90000=3.2328

Answer: 3.2

milcah answered 1 year ago
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