University of New Haven Interaction Plot for Strength Data Means Worksheet

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Mathematics

University of New Haven

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Question 1: A problem in a particle board (or strand board) factory involves producing the strongest 4x8 sheets. There are three variables: pulp concentration at three levels (10, 15, 20), time of cooking the pulp at two levels (1.5, and 2 minutes), and the strand count at three levels (350, 500, and 650). Strength is the dependent variable y. Higher strength is better, 2 samples run at each combination of factors. Data set is on the last page. A. Visually inspect the data. Produce an appropriate individual value plot of the data. Paste it here and Comment on any significant indicators. Paste plot here Comment on individual value plot here or mark the plot: 1 B. Produce a full interaction plot and comment on whether interaction is present. Paste your interaction plot here Comment here on your plot, be specific on why you think there is or is not interaction. 2 C. Run an ANOVA for the complete model including main effects and all two and three-way interactions. Copy / paste the table below and comment on the significant terms (no need to paste the coefficients here too- just the ANOVA table). Include the model summary for r squared and r squared adjusted. In running the model, choose fits and residuals for all observations, 4 in 1 plot, fits and diagnostics for all residuals, and plot residuals versus all the x variables. Use “regular” residuals (not studentized or standardized). You will use this residual information in part (d). ANOVA table here including r squared and r squared adjusted ANOVA Comments needed: what terms are significant and why, use a general benchmark of alpha = 0.05 Comment on R squared and R squared adjusted, and how these values relate to the terms in the ANOVA model 3 D. Analyze residual plots. Choose 4 in one and residuals vs conc. Insert the 4 in 1 plot and comment on the model fit- identify the outliers from the fits and diagnostics table discussed above in the normal plot, versus fits and versus order. 4 in 1 comments Insert residuals versus concentration plot. Comment on the residuals versus concentration plot. Be specific on what you expect to see for a good fit. 4 Problem 1 data Conc 10 10 10 10 10 10 10 10 10 10 10 10 15 15 15 15 15 15 15 15 15 15 15 15 20 20 20 20 20 20 20 20 20 20 20 20 time 1.5 1.5 1.5 1.5 1.5 1.5 2 2 2 2 2 2 1.5 1.5 1.5 1.5 1.5 1.5 2 2 2 2 2 2 1.5 1.5 1.5 1.5 1.5 1.5 2 2 2 2 2 2 strands 350 350 500 500 650 650 350 350 500 500 650 650 350 350 500 500 650 650 350 350 500 500 650 650 350 350 500 500 650 650 350 350 500 500 650 650 Stngth 96.6 96 97.7 96 99.4 99.8 98.4 98.6 99.6 100.4 100.6 100.9 98.5 97.2 96 96.9 98.4 97.6 97.5 98.1 98.7 96 99.6 99 97.5 96.6 95.6 96.2 97.4 98.1 97.6 98.4 97 97.8 98.5 99.8 5
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Question 1:A problem in a particle board (or strand board) factory involves producing the strongest 4x8
sheets. There are three variables: pulp concentration at three levels (10, 15, 20), time of cooking the
pulp at two levels (1.5, and 2 minutes), and the strand count at three levels (350, 500, and 650).
Strength is the dependent variable y. Higher strength is better, 2 samples run at each combination of
factors. Data set is on the last page.
A. Visually inspect the data. Produce an appropriate individual value plot of the data. Paste it here and
Comment on any significant indicators.

Individual Value Plot of Strength
101
100

Strength

99
98
97
96
95
Strand count
Time of cookng the pulp
Pulp Concentration

1.
2.
3.

0 0 0
35 50 65

0 0 0
35 50 65

0 0 0
35 50 65

0 0 0
35 50 65

0 0 0
35 50 65

0 0 0
35 50 65

1.5

0
2.

1.5

0
2.

1.5

0
2.

10

15

20

It can be inferred from the individual plot that higher time of cooking results in highe...


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