Multi linear regression

Multi linear regression

Look at Data Set below. Heat treating is often used to carburize metal parts, such as gears. The thickness of the carburized gear is considered as an important feature of the gear and it 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 involved 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). The data below are the results of the pitch carbon analysis test for 32 parts.

Carry out appropriate analysis to answer the following questions. Show all working.

1)Fit a linear regression model relating the results of the pitch carbon analysis test (PITCH) to the five regressor variables.

2)Test for significance of the regression using an appropriate significance level.

3)Estimate the variance of the model

4)Find the standard errors for the regression coefficients.

5)Evaluate the contribution of each regressor to the model using the t-test with 5% significance level.

6)Plot residuals and comment on model adequacy.

7)Find 95% confidence intervals on the regression coefficients by simulation. Show all steps taken.

8)Using simulation techniques, find a 95% interval on mean PITCH on TEMP=1650, SOAK-TIME=1.00, SOAKPCT=1.10, DIFFTIME=1.00 and DIFFPCT=0.8

9)Using simulation techniques, find a 90% prediction interval fo the observation at the factor levels given above.

10)You are now given the following information.

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