Model Answers to 08 ANOVA in Six Sigma Statistics using Minitab 17, Green Belt Edition.

Set-Up 3

Analysis 3

1. Click Stat<<ANOVA<<General Linear Model<<Fit General Linear Model

Go to the Session window and find the Analysis of Variance table. Look at the P-Value for each of the terms.The P-Values tell us that all of our Factors and Interactions are significant.

The VIFs are less than 5 which means that our model will not suffer from stability issues.

Below that we have the regression equation which we can use to predict values of Sales.

2. Complete the menu as shown below and then click on the Model button.

3. Press the Ctrl key and click on each of the factors to highlight all of  them. Then go the Interactions through order selector and change it to 2. Then click on the Add button.

4. Click OK to return to the root GLM menu.

5.  Click on the Graphs button and select the radio button for the Four-in-One Residual plots.
6. Click OK and OK again to execute the procedure.

The R-sq value tells us that 90.51% of changes in the levels of the factors can be explained by the model.

Finally, to validate the model we must check the residual plots. Find the Four-in-one residual plot in the Graph Window.

 Starting the with Normal Probability plot we want to know if it can be covered with a thick pencil and it can.

The Histogram is not extremely skewed.

The residuals are equally spaced around the zero line on the Versus Fits plot.

The data was collected in time order so using this plot is a valid check.

 We find no patterns in the residuals that would alert us to any problems.

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Set-Up 3

If we look at the Interaction Plot Band5 in Region C gives the highest Sales. But is that the full story?

1. Click Stat<<ANOVA<<General Linear Model<<Comparisons.

2. Complete the menu as shown below and then click OK. To choose the terms for comparisons click on each one to highlight it and then press the ‘C=Compare…’ button.

Analysis 4

Go to the Session window and find the Grouping Information Tables generated by the pairwise comparison.

For Prop_Size, Band5 has the highest Sales but we cannot say it is different to Band4.

For Region, C has the highest Sales but we cannot say it is different to B.

As the interaction term was significant we need to use that to say which levels give the highest sales. Again Band5 C comes out on top. But we cannot say that it is different to the next seven groups.

However, it practise you would probably pick Band5 C as the best and then obtain more results.