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Below, we see a snippet of a dataset that consists of 128 observations and 15 variables. We present two models describing the linear relationship between the BodyFat and other variables. 58.7 37.3 23.4 59.6 38.9 24.0 Density BodyFat Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle 11.0708 12.3 23 154.25 67.75 36.2 93.1 85.2 94.5 59.0 37.3 21.9 2 1.0853 6.1 22 173.25 72.25 38.5 93.6 83.0 98.7 3 1.0414 25.3 22 154.00 66.25 34.0 95.8 87.9 99.2 4 1.0751 10.4 26 184.75 72.25 37.4 101.8 86.4 101.2 5 1.0340 28.7 24 184.25 71.25 34.4 97.3 100.0 101.9 61.0502 20.9 24 210.25 74.75 39.0 104.5 94.4 107.8 Biceps Forearm Wrist 60.1 37.3 22.8 63.2 42.2 24.0 66.0 42.0 25.6 32.0 27.4 17.1 2 30.5 28.9 18.2 3 20.0 25.2 16.6 29.1 18.2 432.4 5 32.2 27.7 27.7 35.7 30.6 10.8 Analysis of Variance Table Model 1: x$BodyFat - x$Neck Model 2: x$BodyFat x$Neck+xSWeight + x$Height F Pr(>F) Res.Df RSS Df Sum of Sq 1 250 13348.1 2 248 9461.4 2 3886.7 50.939 <2.2e-16 *** Signif. codes: 00.001 0.01 0.05 0.11 (b) Let us consider just Hip, Forearm and Wrist as our predictors. How many possible linear models that predict BodyFat can one build? (e) Consider the two models Salary = 6366 +9.3 Age - 329.56 Male, R² = 0.135, ²= 1099 (1) and log(Salary) = 5.342 +0.012 Age - 0.321 Male, R² = 0.178, 8²=1.231. (2) (i) Interpret the coefficient for Male in each model. (ii) Would it be correct to say that the second model is preferred over the first? Explain your reasoning.

Below, we see a snippet of a dataset that consists of 128 observations and 15 variables. We present two models describing the linear relationship between the BodyFat and other variables. 58.7 37.3 23.4 59.6 38.9 24.0 Density BodyFat Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle 11.0708 12.3 23 154.25 67.75 36.2 93.1 85.2 94.5 59.0 37.3 21.9 2 1.0853 6.1 22 173.25 72.25 38.5 93.6 83.0 98.7 3 1.0414 25.3 22 154.00 66.25 34.0 95.8 87.9 99.2 4 1.0751 10.4 26 184.75 72.25 37.4 101.8 86.4 101.2 5 1.0340 28.7 24 184.25 71.25 34.4 97.3 100.0 101.9 61.0502 20.9 24 210.25 74.75 39.0 104.5 94.4 107.8 Biceps Forearm Wrist 60.1 37.3 22.8 63.2 42.2 24.0 66.0 42.0 25.6 32.0 27.4 17.1 2 30.5 28.9 18.2 3 20.0 25.2 16.6 29.1 18.2 432.4 5 32.2 27.7 27.7 35.7 30.6 10.8 Analysis of Variance Table Model 1: x$BodyFat - x$Neck Model 2: x$BodyFat x$Neck+xSWeight + x$Height F Pr(>F) Res.Df RSS Df Sum of Sq 1 250 13348.1 2 248 9461.4 2 3886.7 50.939 <2.2e-16 *** Signif. codes: 00.001 0.01 0.05 0.11 (b) Let us consider just Hip, Forearm and Wrist as our predictors. How many possible linear models that predict BodyFat can one build? (e) Consider the two models Salary = 6366 +9.3 Age - 329.56 Male, R² = 0.135, ²= 1099 (1) and log(Salary) = 5.342 +0.012 Age - 0.321 Male, R² = 0.178, 8²=1.231. (2) (i) Interpret the coefficient for Male in each model. (ii) Would it be correct to say that the second model is preferred over the first? Explain your reasoning.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Below, we see a snippet of a dataset that consists of 128 observations and 15 variables. We present two models describing the linear relationship between the BodyFat and other variables. Density BodyFat Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle 1 1.0708 12.3 23 154.25 85.2 94.5 59.0 37.3 21.9 2 1.0853 6.1 22 173.25 83.0 98.7 58.7 37.3 3 1.0414 87.9 99.2 59.6 38.9 4 1.0751 86.4 101.2 5 1.0340 100.0 101.9 63.2 42.2 6 1.0502 94.4 107.8 66.0 42.0 23.4 24.0 67.75 36.2 93.1 72.25 38.5 93.6 25.3 22 154.00 66.25 34.0 95.8 10.4 26 184.75 72.25 37.4 101.8 28.7 24 184.25 71.25 34.4 97.3 20.9 24 210.25 74.75 39.0 104.5 60.1 37.3 22.8 24.0 25.6 Biceps Forearm Wrist 1 32.0 27.4 17.1 2 30.5 28.9 18.2 3 28.8 25.2 16.6 32.4 29.4 18.2 5 32.2 27.7 17.7 6 35.7 30.6 18.8 Analysis of Variance Table Model 1: x$BodyFat ~ x$Neck Model 2: x$BodyFat x$Neck + xSWeight + x$Height F Pr (>F) Res. Df RSS Df Sum of Sq 1 250 13348.1 2 248 9461.4 2 3886.7 50.939 < 2.2e-16 *** --- Signif. codes: 0*** 0.001 '**' 0.01 0.05 0.11 (b) Let us consider just Hip, Forearm and Wrist as our predictors. How many possible linear models that predict BodyFat can one build? (c) Consider the two models Salary = 6366 +9.3 Age - 329.56 Male, R² = 0.135, ² = 1099 (1) and log(Salary) = 5.342 +0.012 Age -0.321 Male, R² = 0.178, ²= 1.231. (2) (i) Interpret the coefficient for Male in each model. (ii) Would it be correct to say that the second model is preferred over the first? Explain your reasoning.
Transcribed Image Text:Below, we see a snippet of a dataset that consists of 128 observations and 15 variables. We present two models describing the linear relationship between the BodyFat and other variables. Density BodyFat Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle 1 1.0708 12.3 23 154.25 85.2 94.5 59.0 37.3 21.9 2 1.0853 6.1 22 173.25 83.0 98.7 58.7 37.3 3 1.0414 87.9 99.2 59.6 38.9 4 1.0751 86.4 101.2 5 1.0340 100.0 101.9 63.2 42.2 6 1.0502 94.4 107.8 66.0 42.0 23.4 24.0 67.75 36.2 93.1 72.25 38.5 93.6 25.3 22 154.00 66.25 34.0 95.8 10.4 26 184.75 72.25 37.4 101.8 28.7 24 184.25 71.25 34.4 97.3 20.9 24 210.25 74.75 39.0 104.5 60.1 37.3 22.8 24.0 25.6 Biceps Forearm Wrist 1 32.0 27.4 17.1 2 30.5 28.9 18.2 3 28.8 25.2 16.6 32.4 29.4 18.2 5 32.2 27.7 17.7 6 35.7 30.6 18.8 Analysis of Variance Table Model 1: x$BodyFat ~ x$Neck Model 2: x$BodyFat x$Neck + xSWeight + x$Height F Pr (>F) Res. Df RSS Df Sum of Sq 1 250 13348.1 2 248 9461.4 2 3886.7 50.939 < 2.2e-16 *** --- Signif. codes: 0*** 0.001 '**' 0.01 0.05 0.11 (b) Let us consider just Hip, Forearm and Wrist as our predictors. How many possible linear models that predict BodyFat can one build? (c) Consider the two models Salary = 6366 +9.3 Age - 329.56 Male, R² = 0.135, ² = 1099 (1) and log(Salary) = 5.342 +0.012 Age -0.321 Male, R² = 0.178, ²= 1.231. (2) (i) Interpret the coefficient for Male in each model. (ii) Would it be correct to say that the second model is preferred over the first? Explain your reasoning.
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