HW 8

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HW Set 8 Answer Sheet NAME(S): Rylan Crockett, Caivonn Spencer EMGT 446, Six Sigma, Winter 22-23 10 points possible; Topic: DOE: Analysis of Selfie App Data; each problem is worth +0.5 unless indicated otherwise Due Date: Wednesday, 2/8, at midnight in the HW Set 8 Dropbox The set-up for collecting the selfie DATA is in the document HW Set 8 Data Collection . The instructions for this homework set are in the document HW Set 8 Instructions . Please remove any extra blank spaces and make your graphics small, yet readable. 1. A Basic Two-Level Factorial DOE: Using a Selfie App to Determine a Person’s Age Record your team’s three selfie DOE factors and fill out the rest of the requested information for those factors. Factor Name Units Low Level (-) High Level (+) A B C 2. DOE Analysis. Use Minitab’s Assistant to create main effects plots and interaction plots using your team’s three factors. Assistant > DOE > Analyze and Interpret > “Fit Linear Model” – use the target age as your actual age . Copy and paste your team’s main effects plots and interaction plots BELOW. Important: Minitab uses level of significance α = 0.10 to determine whether a factor is significant. I’m not sure why they don’t use α = 0.05! 3(a) Evaluating Main Effects. When you analyze a DOE, you can display main effects plots to visually examine differences in means across factor levels.

Using your team’s main effects plots, which factor(s) appears to have the biggest effect on AGE ? You may not be able to tell exactly since we haven’t done any calculations – you’re just basing your decision on the plots. Minitab makes the background white for factors that are statistically significant at α = 0.10. In addition, a factor may be given a white background simply because it’s a factor with an interaction effect. 3(b) Evaluating Interaction Effects. When you analyze a DOE, you can display interaction effects plots to visually examine differences in means across factor levels. Using your team’s interaction effects plots, which interaction of factors appears to have the biggest effect on AGE? You may not be able to tell exactly since we haven’t done any calculations – you’re just basing your decision on the plots. Minitab makes the background white for interactions that are statistically significant at α = 0.10 . 4. Construct a Cube Plot. Stat > DOE > Factorial > Cube Plot . Use Data Means , the average of your two replicates for each of the 8 unique combinations, as the values for the cube plot and select all your factors. Include the response variable AGE. Copy and paste your team’s Cube Plot HERE. 5. Calculate the main effects for two of your three factors on AGE. Do it by-hand and show your work. Here is how an effect is calculated :

Effect of Factor Y on AGE = ∑ Y + ¿ n + ¿ − ∑ Y − ¿ n − ¿ , ¿ ¿¿ ¿ where n + is the number of values at the “high” level and n - is the number of values at the “low” level. Which team factor are you using? Show your calculations for the effect of that factor: Which team factor are you using? Show your calculations for the effect of that factor: 6. Calculate just ONE interaction effect for your team. Interaction effects are computed using the averages of “opposite” diagonals. Make sure to tell me which interaction effect that you’re calculating for your team. Which two team factors are you using to calculate an interaction effect? Show your calculations for the interaction effect: 7. Construct a half normal plot and a Pareto chart for your team’s DOE. Copy and paste your team’s Pareto and Half Normal plots HERE . Note: Minitab now uses α = 0.05 in determining which factors are significant .

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8. Using the Half Normal and Pareto plots, which factor(s) have the biggest effect on AGE ? Minitab uses level of significance α = 0.05 in determining significant factors in these plots. NOTE: If none of your factors are significant, let me know before moving on. Otherwise, your DOE will be the equation Y = mean of all observations. 9. Next we are finally going to analyze the data with an ANOVA. Calculations in ANOVA determine the significance of each factor based on the effect calculations . In the Session Window, Minitab reports the ANOVA table, standardizes the effects and gives their resulting p -values, and displays the regression model for AGE including all factors. Copy and paste the Coded Coefficients table, ANOVA table, and Model Summary HERE. 10(a) The hypothesis test that is associated with each p -value is the following: H 0 : Factor “ x ” has NO effect on the response (AGE) H a : Factor “ x ” does have an effect on the response (AGE) For a factor to have a statistically significant effect on the response, should it have a small or big p - value? Small Big 10(b) Another way to state the hypothesis test for the Coded Coefficients output is the following: H 0 : Factor’s coefficient is equal to 0 (i.e., factor has no effect) H a : Factor’s coefficient is not equal to 0 (i.e., factor has effect)

Which factors are valid for your team’s model? 11(a) What’s the p -value associated with the “Constant” term in the ANOVA output from #10? 11(b) Does your team’s CONSTANT coefficient, the y -intercept , belong in the regression model according to its p -value? The null hypothesis is: H 0 : Constant coefficient has NO effect on the response (AGE). Yes No 12. The y- intercept represents which of the following? Think back to the Hand-Eye Coordination example – we drew in a dotted line in the Main Effects plots. What was this value? A. The AGE of the selfie taker at an angle of 0. B. The mean AGE of all the trials. C. The AGE that occurred most often when taking selfies. D. The true AGE of the selfie taker. E. The AGE when all factors are set to their lower levels. 13. Copy and paste your team’s original regression equation HERE . This is the equation containing coefficients for ALL factors. 14. After eliminating factors that have “no effect,” unless they are main factors that show up within the interaction effects , copy and paste the new regression equation HERE . 15. Analyze the DOE again: Stat > DOE > Factorial > Analyze Factorial Design. Select the Response as AGE. Now select only the “Terms” that you want to include in your model. Copy and paste your team’s Pareto and Half Normal Plots HERE using only the factors that you are using in your new regression model.

16. Copy and paste the Coded Coefficients, Model Summary, ANOVA table, and Regression Equation in Uncoded Units for the factors that you are keeping in your model HERE . 17. Copy and paste the residual plots HERE. 18-19. [+0.25 for each assumption: +1 total] For your team’s four-in-one residual plots above, are the 4 necessary linear regression model assumptions met? Recall: The assumptions

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necessary to determine that the simple linear regression equation “is legal” are that the residuals are: (1) are normally distributed, (2) centered about 0, (3) have constant variance across the fitted values, and (4) are independent and identically distributed with respect to order of observation. Please briefly state reasons why you believe each assumption is or is not met with respect to your team’s residuals plot. Be specific – for example, for Team Benjamin Button’s plots, I would say “the normality plot only has one point that makes me question normality – but I believe the data is from a normally distributed population.” Similarly, “the time ordered plot of the residuals does look random (except for that one point), so the residuals do appear to be IID.” If you’ve forgotten how to read the 4-in-1 plot, please just ask me. 20. Let’s say your team wants to be able to hit the target age you set at xx years old – what combination of factors should you use in your final regression model? Well … this is kind of a boring question because we are only using categorical variables at 2 levels, so Minitab’s optimizer is just going to pick the combination of factors that is closest to the target (AGE) that you want to hit. Use Stat > DOE > Factorial > Results Optimizer: Solution Solutio n Angl e Eyewear AGE Fit Composit e Desirabili ty 1 Belo w No glasses 32.7 5 0.925 For Team Benjamin Buttons – the combo giving the closest value to 32 (his real age at the time) would be Angle: Below, Eyewear: No Glasses. You can also ask Minitab to find the combo for the Minimum or Maximum Age as well. Your team wants to come as close as possible to ______ years old; what combination should you use?

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