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 and consider which are significant.

The P-Values are telling us that the Factors Press and Temp are significant. It does not matter which material we use to make the phone. Neither the 2-way or the single 3-way interactions are significant. Removing all non-significant terms from the model is the next step.

In the Session Window we find that the Analysis of Variance table only has significant terms. As we have reduced the number of terms the Lack-of-Fit p-Value has appeared. It tells us that the model does fit the data.

Set-Up 4

1. Click Stat<<ANOVA<<General Linear Model<<Fit General Linear Model or press Ctrl+E.

Analysis 4

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 3. Then click on the Add button.

4. Click OK & OK to execute the procedure.

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

2. Remove Material as a Factor  and then click on the Model button.

3. Minitab will remove all interactions apart from the ‘Temp*Press’  interaction. Remove that by pressing the Default button. Then return to the root GLM menu by clicking OK once.

The R-sq value tells us that 87.6% of changes in the levels of the factors can be explained by the model.

As only Temp and Press are the significant factors we can use the Main Effects plot to establish which setting would give the greatest strength;  Temp=115, Press=7.

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 strength.

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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