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In: Statistics and Probability

Heat treating is often used to carburize metal parts, such as gears. The thickness of the...

Heat treating is often used to carburize metal parts, such as gears. The thickness of the carburized layer is considered a crucial feature of the gear and contributes to the overall reliability of the part. Because of the critical nature of this feature, two different lab tests are performed on each furnace load. One test is run on a sample pin that accompanies each load. The other test is a destructive test, where an actual part is cross-sectioned. This test involves running a carbon analysis on the surface of both the gear pitch (top of the gear tooth) and the gear root (between the gear teeth). Table 12-6 shows the results of the pitch carbon analysis test for 32 parts.

Temp

SoakTime

SoakPct

DiffTime

DiffPct

Pitch

1650

0.58

1.1

0.25

0.9

0.013

1650

0.66

1.1

0.33

0.9

0.016

1650

0.66

1.1

0.33

0.9

0.015

1650

0.66

1.1

0.33

0.95

0.016

1600

0.66

1.15

0.33

1

0.015

1600

0.66

1.15

0.33

1

0.016

1650

1

1.1

0.5

0.8

0.014

1650

1.17

1.1

0.58

0.8

0.021

1650

1.17

1.1

0.58

0.8

0.018

1650

1.17

1.1

0.58

0.8

0.019

1650

1.17

1.1

0.58

0.9

0.021

1650

1.17

1.1

0.58

0.9

0.019

1650

1.17

1.15

0.58

0.9

0.021

1650

1.2

1.15

1.1

0.8

0.025

1650

2

1.15

1

0.8

0.025

1650

2

1.1

1.1

0.8

0.026

1650

2.2

1.1

1.1

0.8

0.024

1650

2.2

1.1

1.1

0.8

0.025

1650

2.2

1.5

1.1

0.8

0.024

1650

2.2

1.1

1.1

0.9

0.025

1650

2.2

1.1

1.1

0.9

0.027

1650

2.2

1.1

1.5

0.9

0.026

1650

3

1.15

1.5

0.8

0.029

1650

3

1.1

1.5

0.7

0.03

1650

3

1.1

1.5

0.75

0.028

1650

3

1.15

1.66

0.85

0.032

1650

3.33

1.1

1.5

0.8

0.033

1700

4

1.1

1.5

0.7

0.039

1650

4

1.1

1.5

0.7

0.04

1650

4

1.15

1.5

0.85

0.035

1700

12.5

1

1.5

0.7

0.056

1700

18.5

1

1.5

0.7

0.068

PLEASE answer only the STEPWISE part of the question

Repeat steps (a)-(d) except utilize stepwise regression to identify a model.]

  1. Fit a regression model using all five regressors. Write out the equation. Summarize this analysis by providing the equation, ?2, and list the standard errors.    What does the analysis of variance indicate?
  2. Check for multicollinearity. Explain your findings.
  3. Describe what you notice about the p values for the regressors. Construct a t-test on each regression coefficient. What can you conclude about the variables in this model? Use an alpha = 0.05.
  4. Prepare a normal probability plot of the residuals and check the adequacy of the model.

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