Model Answers to 12 Regression in Six Sigma Statistics using Minitab 17, Green Belt Edition.

Exercise 12.7.2  Multiple Regression

Data has been collected on a process where four predictors are thought to affect a single continuous Response variable. The data has not been collected in time order. Conduct the appropriate Regression analysis and answer the questions below.

The data in File 12 Regression.xlsx worksheet Exercise2.

  1. Are any of the predictors correlated?
  2. Are all the predictors significant?
  3. How much of the variation in the Response can be explained by changes in the Predictors?
  4. What terms are present in the model?
  5. Are there any unusual data points in the study and are they an issue?
  6. What are the top solutions to obtain a value of 200 in the Response?

Set-Up 1

Analysis 1

  1. Click Stat<<Basic Stats<<Correlation.
  2. Enter the 4 predictors so we can check if they are correlated.
  3. Click OK.
  4. Go to the Session Window to check the results.

The P-Values indicate that there are no significant correlations.

On the top left of the Summary Report we are told that the model is significant and that 87.46% of the changes in the response can be explained by changes in the predictor.

Set-Up 2

  1. Click Assistant<<Regression. Click on the Optimize Response   box.
  2. Enter Response as the response.
  3. Select ‘Achieve a target value’ from the drop-down menu and set ‘200’ as the target.
  4. Enter Pred1 to Pred4 as the four predictor variables.
  5. Click OK to run the procedure and produce the 6 page report.

Analysis 2

On the Diagnostic Report we see the Residuals vs Fitted Values plot. On this we are shown two points with large residuals and 3 points with unusual X values. We should review the data collected at these points to check for anything unusual.

From the Model Building Report we are given the Regression Equation and we can see that it has five terms. Predictor 4 was not included as it was not significant.

The Prediction and Optimisation Report shows us an optimal setting to achieve a response of 200. It was gives us 5 alternate settings.

The Report Card warns us of the large residuals and Unusual X values. It would be prudent to check any history on those 5 data points that have been highlighted.