Question

The purpose is to work through an analysis of the data using several different regression techniques....

The purpose is to work through an analysis of the data using several different regression techniques. The data are as follows:

Temp

Soak Time

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

Questions

  1. State the problem—what are you trying to find out?
  2. Fit a regression model using all of the five regressors. Summarize this analysis by providing the equation, ?2, and list the standard errors. What do you notice about the p values for the regressors? What does the analysis of variance indicate?
  3. Use the model to predict PITCH when TEMP=1650, SOAKTIME=1, SOAKPCT=1.1, DIFFTIME=1 and DIFFPCT=.8.
  4. Do you have any problems with multicollinearity?
  5. Construct a t-test on each regression coefficient. What can you conclude about the variables in this model? Use an alpha = 0.0
  6. Find a 95% confidence interval on each of the coefficients that were identified to be significant. Also construct a confidence interval and prediction interval on the future observation for the data given in Q3.
  7. Prepare a normal probability plot of the residuals and check the adequacy of the model.
  8. Utilize stepwise regression to identify a model. How does this model differ from the first one you created? Construct a normal probability plot on the residuals to check model adequacy. Write out the equation.
  9. What are the possible benefits of using a model that has fewer regressors?
Math   Statistics-And-Probability   
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