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Verbal Subtest Vocabulary Similarities Arithmetic Digit Span Information Comprehension Letter-Number Sequencing Performance Subtest Picture Completion Digit Symbol-Coding Block Design Matrix Reasoning Picture Arrangement Symbol Search Object Assembly

[Pri04]

(c) Compute the standard errors of the regression coefficients. (d) Predict power consumption for a month in which x1 75 F, x2 24 days, x3 90%, and x4 98 tons. 12-7. A study was performed on wear of a bearing y and its relationship to x1 oil viscosity and x2 load. The following data were obtained. y 293 230 172 91 113 125 x1 1.6 15.5 22.0 43.0 33.0 40.0 x2 851 816 1058 1201 1357 1115

Strength or Weakness (S or W)

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(a) Fit a multiple linear regression model using x2, x3, x4, and x5 as the regressors. (b) Estimate 2. (c) Find the se( j). How precisely are the regression coefficients estimated, in your opinion (d) Use the model from part (a) to predict pull strength when x2 = 20, x3 = 30, x4 = 90, and x5 = 2.0. 12-9. An engineer at a semiconductor company wants to model the relationship between the device HFE ( y) and three parameters: Emitter-RS (x1), Base-RS (x2), and Emitter-to-Base RS (x3). The data are shown in the following table. x1 Emitter-RS 14.620 15.630 14.620 15.000 14.500 15.250 16.120 15.130 15.500 15.130 15.500 16.120 15.130 15.630 15.380 14.380 15.500 14.250 14.500 14.620 x2 Base-RS 226.00 220.00 217.40 220.00 226.50 224.10 220.50 223.50 217.60 228.50 230.20 226.50 226.60 225.60 229.70 234.00 230.00 224.30 240.50 223.70 x3 E-B-RS 7.000 3.375 6.375 6.000 7.625 6.000 3.375 6.125 5.000 6.625 5.750 3.750 6.125 5.375 5.875 8.875 4.000 8.000 10.870 7.375 y HFE-1M-5V 128.40 52.62 113.90 98.01 139.90 102.60 48.14 109.60 82.68 112.60 97.52 59.06 111.80 89.09 101.00 171.90 66.80 157.10 208.40 133.40

[Pry97]

9 5 14 13 14 6 11

(a) Fit a multiple linear regression model to these data. (b) Estimate 2 and the standard errors of the regression coefficients. (c) Use the model to predict wear when x1 25 and x2 1000. (d) Fit a multiple linear regression model with an interaction term to these data. (e) Estimate 2 and se( j) for this new model. How did these quantities change. Does this tell you anything about the value of adding the interaction term to the model (f) Use the model in (d) to predict when x1 25 and x2 1000. Compare this prediction with the predicted value from part (b) above. 12-8. The pull strength of a wire bond is an important characteristic. The following table gives information on pull strength ( y), die height (x1), post height (x2), loop height (x3), wire length (x4), bond width on the die (x5), and bond width on the post (x6). y 8.0 8.3 8.5 8.8 9.0 9.3 9.3 9.5 9.8 10.0 10.3 10.5 10.8 11.0 11.3 11.5 11.8 12.3 12.5 x1 5.2 5.2 5.8 6.4 5.8 5.2 5.6 6.0 5.2 5.8 6.4 6.0 6.2 6.2 6.2 5.6 6.0 5.8 5.6 x2 19.6 19.8 19.6 19.4 18.6 18.8 20.4 19.0 20.8 19.9 18.0 20.6 20.2 20.2 19.2 17.0 19.8 18.8 18.6 x3 29.6 32.4 31.0 32.4 28.6 30.6 32.4 32.6 32.2 31.8 32.6 33.4 31.8 32.4 31.4 33.2 35.4 34.0 34.2 x4 94.9 89.7 96.2 95.6 86.5 84.5 88.8 85.7 93.6 86.0 87.1 93.1 83.4 94.5 83.4 85.2 84.1 86.9 83.0 x5 2.1 2.1 2.0 2.2 2.0 2.1 2.2 2.1 2.3 2.1 2.0 2.1 2.2 2.1 1.9 2.1 2.0 2.1 1.9 x6 2.3 1.8 2.0 2.1 1.8 2.1 1.9 1.9 2.1 1.8 1.6 2.1 2.1 1.9 1.8 2.1 1.8 1.8 2.0

(a) Fit a multiple linear regression model to the data. (b) Estimate 2. (c) Find the standard errors se 1 j 2. (d) Predict HFE when x1 14.5, x2 220, and x3 5.0. 12-10. Heat treating is often used to carburize metal parts, such as gears. The thickness of the carburized layer is considered a crucial feature of the gear and contributes to the overall reliability of the part. Because of the critical nature of this feature, two different lab tests are performed on each furnace load. One test is run on a sample pin that accompanies each load. The other test is a destructive test, where an actual part is cross-sectioned. This test involves running a carbon analysis on the surface of both the gear pitch (top of the gear tooth) and the gear root (between the gear teeth). Table 12-7 shows the results of the pitch carbon analysis test for 32 parts. The regressors are furnace temperature (TEMP), carbon concentration and duration of the carburizing cycle

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