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

Part I: Problem Definition Describe the company's needs and how you can to use the data to solve it.

Part II: Methods In this section describe the data and methods used to solve the company's production problem. Be sure to include the work for any calculations you do. As part of your answer, specifically include these tasks.

1) Fit a regression model using all five regressors. Include the following

a. The equation

b. Value of 2

c. Values of the standard errors

d. ANOVA results

e. VIF values

f. P-values and T-test on each regression coefficient. Use = 0.05.

g. Normal probability plot of the residuals

h. R 2

2) Repeat (a)-(g) from item (1) except utilize stepwise regression to identify a model.

3) Use each model to predict PITCH when TEMP=1650, SOAKTIME=1, SOAKPCT=1.1, DIFFTIME=1 and DIFFPCT=0.8. Also construct a confidence interval for these predicted values.

4) Construct a 95% confidence interval on each of the coefficients that were identified to be significant.

Part III: Conclusions and Recommendations In this section explain what you conclude from Part II. Your discussion should include the followings aspects of each model: a. Significance of the model b. Multicollinearity c. Conclusions about the variables in this model. Use = 0.05. d. Normality of the residuals e. Adequacy of the model