Homework11Solns - Stat 512 2 Solutions to Homework #11 Dr....

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Stat 512 – 2 Solutions to Homework #11 Dr. Simonsen Due Wednesday, November 16, 2005, by 4:30pm For these problems use the Electronics Assembly data described in problem 24.12 on page 1025 of KNNL (this is 23.12 in NKNW). 1. Run the full three-way analysis of variance for these data, and check the assumptions. Summarize the results of the hypothesis tests for main and interaction effects, and your conclusions regarding the assumptions. Dependent Variable: time Sum of Source DF Squares Mean Square F Value Pr > F Model 11 973645.933 88513.267 103.16 <.0001 Error 48 41186.000 858.042 Corrected Total 59 1014831.933 R-Square Coeff Var Root MSE time Mean 0.959416 2.760738 29.29235 1061.033 Source DF Type I SS Mean Square F Value Pr > F gender 1 540360.6000 540360.6000 629.76 <.0001 seq 2 49319.6333 24659.8167 28.74 <.0001 gender*seq 2 542.5000 271.2500 0.32 0.7305 exper 1 382401.6667 382401.6667 445.67 <.0001 gender*exper 1 91.2667 91.2667 0.11 0.7457 seq*exper 2 911.2333 455.6167 0.53 0.5914 gender*seq*exper 2 19.0333 9.5167 0.01 0.9890 The main effects for gender, seq, and experience are all significant, but none of the interactions are significant. resid -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 gender 12 0 seq 123
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resid -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 exper 12 0 pr edi ct 800 900 1000 1100 1200 1300 -3 -2 -1 0 1 2 3 0 r e s i d Nor mal Quant i l es 10 30 50 0 5 15 25 35 P e r c e n t The variance appears to be fairly constant, though in the residual plot for experience the variance appears somewhat smaller for the lower experience level. The normality assumption appears to be mildly violated, with a slight s-shape to the qqplot (and a somewhat flattened histogram). However, the violation does not seem to be too severe. 2. Although the response variable Y was originally measured as the time in minutes to assemble 50 boards, the experimenter felt that the transformed variable 50 60 3000 Y YY × == was more easily interpretable as the speed of assembly in units of number of boards per hour. Run the three-way analysis using Y as the response variable, and check the assumptions. Summarize the results of the hypothesis tests for main and interaction effects, and your conclusions regarding the assumptions. Dependent Variable: speed Sum of Source DF Squares Mean Square F Value Pr > F Model 11 7.44678423 0.67698038 100.68 <.0001 Error 48 0.32274770 0.00672391 Corrected Total 59 7.76953192 R-Square Coeff Var Root MSE speed Mean 0.958460 2.855971 0.081999 2.871158
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Source DF Type I SS Mean Square F Value Pr > F gender 1 4.04423554 4.04423554 601.47 <.0001 seq 2 0.37791814 0.18895907 28.10 <.0001 gender*seq 2 0.01167385 0.00583692 0.87 0.4262 exper 1 2.90396052 2.90396052 431.89 <.0001 gender*exper 1 0.07733581 0.07733581 11.50 0.0014 seq*exper 2 0.03026494 0.01513247 2.25 0.1163 gender*seq*exper 2 0.00139542 0.00069771 0.10 0.9016 The main effects of gender, seq, and experience are all significant. In addition, the interaction effect of gender by experience is also significant. The interactions of gender by seq, seq by experience, and the three-way interaction are not significant. resid -0.20 -0.18 -0.16 -0.14 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 0. 00 0. 02 0. 04 0. 06 0. 08 0. 10 0. 12 0. 14 0. 16 0. 18 0. 20 gender 12 seq 123 exper pr edi ct 2. 3 2. 4 2. 5 2. 6 2. 7 2. 8 2. 9 3. 0 3. 1 3. 2 3. 3 3. 4 3. 5 -3 -2 -1 0 1 2 3 -0.2 -0.1 0 0. 1 0. 2 r e s i d Nor mal Quant i l es - 0. 18 - 0. 12 - 0. 06 0 0 5 10 15 20 25 30 35 P e r c e n t
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The constant variance assumption appears to be violated somewhat, as can be seen in the plots vs.
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This note was uploaded on 02/02/2012 for the course STAT stat512 taught by Professor Libo during the Spring '11 term at Purdue North Central.

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Homework11Solns - Stat 512 2 Solutions to Homework #11 Dr....

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