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.

Attached file has the answers requirement and the table

EMGT 6100 Problem Scenario 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 1650 1650 1650 1650 1600 1600 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1700 1650 SoakTime 0.58 0.66 0.66 0.66 0.66 0.66 1 1.17 1.17 1.17 1.17 1.17 1.17 1.2 2 2 2.2 2.2 2.2 2.2 2.2 2.2 3 3 3 3 3.33 4 4 SoakPct 1.1 1.1 1.1 1.1 1.15 1.15 1.1 1.1 1.1 1.1 1.1 1.1 1.15 1.15 1.15 1.1 1.1 1.1 1.15 1.1 1.1 1.1 1.15 1.1 1.1 1.15 1.1 1.1 1.1 DiffTime 0.25 0.33 0.33 0.33 0.33 0.33 0.5 0.58 0.58 0.58 0.58 0.58 0.58 1.1 1 1.1 1.1 1.1 1.1 1.1 1.1 1.5 1.5 1.5 1.5 1.66 1.5 1.5 1.5 DiffPct 0.9 0.9 0.9 0.95 1 1 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.8 0.7 0.75 0.85 0.8 0.7 0.7 Pitch 0.013 0.016 0.015 0.016 0.015 0.016 0.014 0.021 0.018 0.019 0.021 0.019 0.021 0.025 0.025 0.026 0.024 0.025 0.024 0.025 0.027 0.026 0.029 0.03 0.028 0.032 0.033 0.039 0.04 1650 1700 1700 4 12.5 18.5 1.15 1 1 1.5 1.5 1.5 0.85 0.7 0.7 0.035 0.056 0.068 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. a) 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? b) Check for multicollinearity. Explain your findings. c) Describe what you notice about the p values for the regressors. Construct a ttest on each regression coefficient. What can you conclude about the variables in this model? Use an alpha = 0.05. d) Prepare a normal probability plot of the residuals and check the adequacy of the model. e) Repeat steps (a)-(d) except utilize stepwise regression to identify a model