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Researchers at a large nutrition and weight management company are trying to build a model to predict a person’s body fat percentage from an array of variables such as body weight, height, and body measurements around the neck, chest, abdomen, hips, biceps, etc. A variables selection method is used to build a regression model. The final model is shown . Question: What percentage of the variation in percent body fat remains unexplained, even after introducing weight and abdomen circumference into the model? Also state interpretation of the slope for weight.

Researchers at a large nutrition and weight management company are trying to build a model to predict a person’s body fat percentage from an array of variables such as body weight, height, and body measurements around the neck, chest, abdomen, hips, biceps, etc. A variables selection method is used to build a regression model. The final model is shown . Question: What percentage of the variation in percent body fat remains unexplained, even after introducing weight and abdomen circumference into the model? Also state interpretation of the slope for weight.

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
Problem 1P
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Researchers at a large nutrition and weight management company are trying to build a model to predict a person’s body fat percentage from an array of variables such as body weight, height, and body measurements around the neck, chest, abdomen, hips, biceps, etc. A variables selection method is used to build a regression model. The final model is shown .

Question: What percentage of the variation in percent body fat remains unexplained, even after introducing weight and abdomen circumference into the model? Also state interpretation of the slope for weight.

 

The image contains two tables detailing a statistical output, likely from a regression analysis. ### Table 1: ANOVA Summary - **Source:** - **Model** - DF: 2 - Sum of Squares: 3053.290 - Mean Square: 1526.645 - F Value: 129.239 - Pr > F: 0.0000 - **Error** - DF: 46 - Sum of Squares: 543.379 - Mean Square: 11.813 - **Corrected Total** - DF: 48 - Sum of Squares: 22617.000 ### Interpretation: This table shows the ANOVA (Analysis of Variance) results. The F Value of 129.239 and a p-value (Pr > F) of 0.0000 indicates that the model is statistically significant. ### Table 2: Regression Coefficients - **Metrics:** - **R-Square:** 0.8499 - **Root MSE:** 3.4369 - **Parameter estimates:** - **Intercept** - Estimate: -53.954 - Standard Error: 4.742 - t Value: -11.379 - Pr > |t|: 0.0000 - **Weight** - Estimate: -0.162 - Standard Error: 0.038 - t Value: -4.230 - Pr > |t|: 0.0002 - **Abdomen circumference** - Estimate: 1.105 - Standard Error: 0.101 - t Value: 10.912 - Pr > |t|: 0.0000 ### Interpretation: The second table provides details on the regression coefficients. The high R-Square value of 0.8499 indicates that a large portion of the variability in the outcome can be explained by the model. All parameters have statistically significant p-values (less than 0.05), suggesting that they are significant predictors in the model.
Transcribed Image Text:The image contains two tables detailing a statistical output, likely from a regression analysis. ### Table 1: ANOVA Summary - **Source:** - **Model** - DF: 2 - Sum of Squares: 3053.290 - Mean Square: 1526.645 - F Value: 129.239 - Pr > F: 0.0000 - **Error** - DF: 46 - Sum of Squares: 543.379 - Mean Square: 11.813 - **Corrected Total** - DF: 48 - Sum of Squares: 22617.000 ### Interpretation: This table shows the ANOVA (Analysis of Variance) results. The F Value of 129.239 and a p-value (Pr > F) of 0.0000 indicates that the model is statistically significant. ### Table 2: Regression Coefficients - **Metrics:** - **R-Square:** 0.8499 - **Root MSE:** 3.4369 - **Parameter estimates:** - **Intercept** - Estimate: -53.954 - Standard Error: 4.742 - t Value: -11.379 - Pr > |t|: 0.0000 - **Weight** - Estimate: -0.162 - Standard Error: 0.038 - t Value: -4.230 - Pr > |t|: 0.0002 - **Abdomen circumference** - Estimate: 1.105 - Standard Error: 0.101 - t Value: 10.912 - Pr > |t|: 0.0000 ### Interpretation: The second table provides details on the regression coefficients. The high R-Square value of 0.8499 indicates that a large portion of the variability in the outcome can be explained by the model. All parameters have statistically significant p-values (less than 0.05), suggesting that they are significant predictors in the model.
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