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 7 months ago
Next > < Previous

Related Solutions

Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0.  elsewhere (a) Find the...
Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0.  elsewhere (a) Find the conditional densities (pdf) of X1|X2 = x2 and X2|X1 = x1. (b) Find the conditional expectation and variance of X1|X2 = x2 and X2|X1 = x1. (c) Compare the probabilities P(0 < X1 < 1/2|X2 = 3/4) and P(0 < X1 < 1/2). (d) Suppose that Y = E(X2|X1). Verify that E(Y ) = E(X2), and that var(Y ) ≤ var(X2).
Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf                    f(x1, x2)...
Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf                    f(x1, x2) = 4x1(1-x2) ,     0<x1<1 0<x2<1                                       0,                  otherwise (ii) For the same joint pdf, calculate E(X1X2) and E(X1 + X2) (iii) Calculate Var(X1X2)
Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary
  Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow. Repair Time in Hours Months Since Last Service Type of Repair Repairperson 2.9 2 Electrical Dave Newton 3 6 Mechanical Dave Newton 4.8 8 Electrical Bob Jones 1.8...
Let X1 and X2 be independent standard normal variables X1 ∼ N(0, 1) and X2 ∼...
Let X1 and X2 be independent standard normal variables X1 ∼ N(0, 1) and X2 ∼ N(0, 1). 1) Let Y1 = X12 + X12 and Y2 = X12− X22 . Find the joint p.d.f. of Y1 and Y2, and the marginal p.d.f. of Y1. Are Y1 and Y2 independent? 2) Let W = √X1X2/(X12 +X22) . Find the p.d.f. of W.
   3. (i) Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf...
   3. (i) Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf                    f(x1, x2) = 4x1(1-x2) ,     0<x1<1 0<x2<1                                       0,                  otherwise (ii) For the same joint pdf, calculate E(X1X2) and E(X1 + X2) (iii) Calculate Var(X1X2)
given the sequences  x1 = [2, 6, -4, 1] x2 = [8, 0, 2, 0, -9,...
given the sequences  x1 = [2, 6, -4, 1] x2 = [8, 0, 2, 0, -9, 0, 1, 0] x3 = [2, 0, -8, -8, 2] x4 = [0, 1, 5i, 0, 6i, 0] x5 = [9, 3, 7] plot the 1. DFT magnitude of the computed sequences in MATLAB  2. phase responses in degrees and radians against frequency and number of samples 3. comment on the plots
1. Let X1 and X2 be continuous distributions uniformly distributed across the region [0, 2] ×...
1. Let X1 and X2 be continuous distributions uniformly distributed across the region [0, 2] × [0, 2] U (2, 4] × (2, 4]. a) Find the joint probability density function as well as marginal probability density function of X1 and X2. b) Prove that X1 and X2 are not independent by showing cov(X1, X2) != 0.
1. Let X1, X2 be i.i.d with this distribution: f(x) = 3e cx, x ≥ 0...
1. Let X1, X2 be i.i.d with this distribution: f(x) = 3e cx, x ≥ 0 a. Find the value of c b. Recognize this as a famous distribution that we’ve learned in class. Using your knowledge of this distribution, find the t such that P(X1 > t) = 0.98. c. Let M = max(X1, X2). Find P(M < 10)
DATA 2 ID X1 X2 X3 Y A 0 2 4 9 B 1 0 8...
DATA 2 ID X1 X2 X3 Y A 0 2 4 9 B 1 0 8 10 C 0 1 0 5 D 1 1 0 1 E 0 0 8 10 CORRELATION MATRIX Y X1 X2 X3 Y 1 ? -0.304 +0.889 X1 ? 1 -0.327 0 X2 -0.304 -0.327 1 -0.598 X3 +0.889 0 -0.598 1 1. What is the sum of squares regression for the full model? (Correct answer is 58, please show me how to get...
DATA 2 ID X1 X2 X3 Y A 0 2 4 9 B 1 0 8...
DATA 2 ID X1 X2 X3 Y A 0 2 4 9 B 1 0 8 10 C 0 1 0 5 D 1 1 0 1 E 0 0 8 10 CORRELATION MATRIX Y X1 X2 X3 Y 1 ? -0.304 +0.889 X1 ? 1 -0.327 0 X2 -0.304 -0.327 1 -0.598 X3 +0.889 0 -0.598 1 Comparing the zero order model and full model 1. Did the addition of X2 and X3 significantly increase R2? (correct answer is...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT