Question 5 [ 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 Body Fat and other variables. Hip Thigh Enee Ankle Density BodyFat Age Weight Height Neck Chest Abdomen 85.2 94.5 59.0 37.3 21.9 93.1 1 1.0708 12.3 23 154.25 67.75 36.2 83.0 98.7 58.7 37.3 23.4 93.6 6.1 22 173.25 72.25 30.5 87.9 99.2 59.6 38.9 24.0 25.3 22 154.00 66.25 34.0 95.8 56.4 101.2 10.4 26 104.75 72.25 37.4 101.8 *** 100.0 101.9 63.2 42.2 24.0 28.7 24 184.25 71.25 34.4 97.3 54.4 207.8 66.0 42.0 25.6 20.9 24 210.25 74.75 39.0 104.5 60.1 37.3 22.0 4 1.0853 1.0414 1.0751 1.0340 **** 4.0502 S 6 Biceps Forearm Wrist 4 32.0 27.5 17.1 28.9 18.2 2 30.5 3 26.8 25.2 16.6 4 32.4 29.4 18.2 5 32.2 27.7 17.7 6 35.7 30.6 18.8 (a) By looking at the R output, state whether one should include extra parameters in the model. Page 8 Analysis of Variance Table Model 1: x$BodyFat x$Neck Model 2: x$BodyFat x$Neck+xSWeight + x$Height Res. Df RSS Df Sum of Sq Pr (>F) F 1 250 13348.1 2 248 9461.4 2 3886.7 50.939 <2.2e-16*** Signif. codes: 00.001 0.01 0.05 0.1'' 1 (b) Let us consider just Hip, Forearned Wrist as our predictors. How many possible linear models that predict Body Fat can one build? (c) Consider the two models Salary=6366+9.3 Age-329.56 Male, R²=0.135, ²=1099 and log (Salary)=5.342 +0.012 Age-0.321 Male, R=0.178, 1.231. (2) (i) Interpret the coefficient for Male in each model. (i) Would it be correct to say that the second model is preferred over the first? Explain your reasoning. Consider another model log(Salary)=3.54+0.127 Age-0.321 Male, R=0.880, ² = 0.757 (3) (iii) Is model (3) better than model (2)? Why?
Question 5 [ Below, we see a snippet of a dataset that consists of 128 observations and 15 variables. We present two models describing the linear relationship between the Body Fat and other variables. Hip Thigh Enee Ankle Density BodyFat Age Weight Height Neck Chest Abdomen 85.2 94.5 59.0 37.3 21.9 93.1 1 1.0708 12.3 23 154.25 67.75 36.2 83.0 98.7 58.7 37.3 23.4 93.6 6.1 22 173.25 72.25 30.5 87.9 99.2 59.6 38.9 24.0 25.3 22 154.00 66.25 34.0 95.8 56.4 101.2 10.4 26 104.75 72.25 37.4 101.8 *** 100.0 101.9 63.2 42.2 24.0 28.7 24 184.25 71.25 34.4 97.3 54.4 207.8 66.0 42.0 25.6 20.9 24 210.25 74.75 39.0 104.5 60.1 37.3 22.0 4 1.0853 1.0414 1.0751 1.0340 **** 4.0502 S 6 Biceps Forearm Wrist 4 32.0 27.5 17.1 28.9 18.2 2 30.5 3 26.8 25.2 16.6 4 32.4 29.4 18.2 5 32.2 27.7 17.7 6 35.7 30.6 18.8 (a) By looking at the R output, state whether one should include extra parameters in the model. Page 8 Analysis of Variance Table Model 1: x$BodyFat x$Neck Model 2: x$BodyFat x$Neck+xSWeight + x$Height Res. Df RSS Df Sum of Sq Pr (>F) F 1 250 13348.1 2 248 9461.4 2 3886.7 50.939 <2.2e-16*** Signif. codes: 00.001 0.01 0.05 0.1'' 1 (b) Let us consider just Hip, Forearned Wrist as our predictors. How many possible linear models that predict Body Fat can one build? (c) Consider the two models Salary=6366+9.3 Age-329.56 Male, R²=0.135, ²=1099 and log (Salary)=5.342 +0.012 Age-0.321 Male, R=0.178, 1.231. (2) (i) Interpret the coefficient for Male in each model. (i) Would it be correct to say that the second model is preferred over the first? Explain your reasoning. Consider another model log(Salary)=3.54+0.127 Age-0.321 Male, R=0.880, ² = 0.757 (3) (iii) Is model (3) better than model (2)? Why?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 5
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 Body Fat and other variables.
Density BodyFat Age Weight Height Neck Chest Abdomen
1.0708 12.3 23 154.25 67.75 36.2 93.1
1
2 1.0853
Hip Thigh Enee Ankle
59.0 37.3 21.9
58.7 37.3 23.4
59.6 38.9 24.0
6.1
25.3
10.4
3 1.0414
85.2 94.5
83.0 98.7
87.9 99.2
96.4 101.2
22 173.25
22 154.00
26 184.75
40
72.25 38.5 93.6
66.25 34.0 95.8
72.25 37.4 101.8
71.25 34.4 97.3
74.75 39.0 104.5
60.1 37.3 22.0
4
1.0751
1.0340
6 1.0502
5
100.0 101.9 63.2 42.2 24.0
94.4 107.8 66.0 42.0 25.6
28.7 24 184.25
20.9 24 210.25
20.9
Biceps Forearm Wrist
1
32.0
30.5
27.4 17.1
27.417-2
28.9 18.2
25.2 16.6
3
26.8
4
32.4
29.4 18.2
5
32.2
27.7 17.7
6
35.7 30.6 18.8
(a) By looking at the R output, state whether one should include extra parameters in
the model.
Page 8
Analysis of Variance Table
Model 1: x$BodyFat x$Neck
Model 2: x$BodyFat x$Neck + xSWeight
Res.Df RSS Df Sum of Sq
+ x$Height
F
Pr (>F)
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 0.1''1
(b) Let us consider just Hip, Forearned Wrist as our predictors. How many
possible linear models that predict Body Fat can one build?
(c) Consider the two models
Salary=6366+9.3 Age-329.56 Male, R²=0.135, 8²=1099 (1)
and
log(Salary)=5.342 +0.012 Age-0.321 Male, R=0.178, 8²1.231. (2)
(i) Interpret the coefficient for Male in each model.
(i) Would it be correct to say that the second model is preferred over the first?
Explain your reasoning.
Consider another model
log(Salary)=3.54+0.127 Age-0.321 Male, R=0.880, 0.757. (3)
(iii) Is model (3) better than model (2)? Why?
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