Question

D.48  Predicting Percent Body Fat

Data 10.1 introduces the dataset BodyFat. Computer output is shown for using this sample to create a multiple regression model to predict percent body fat using the other nine variables.

Predictor

	Coef	SE Coef	T	P
The regression equation is Bodyfat = − 23.7 + 0.0838 Age − 0.0833 Weight + 0.036 Height + 0.001 Neck − 0.139 Chest + 1.03 Abdomen + 0.226 Ankle + 0.148 Biceps − 2.20 Wrist
Constant	−23.66	29.46	−0.80	0.424
Age	0.08378	0.05066	1.65	0.102
Weight	−0.08332	0.08471	−0.98	0.328
Height	0.0359	0.2658	0.14	0.893
Neck	0.0011	0.3801	0.00	0.998
Chest	−0.1387	0.1609	−0.86	0.391
Abdomen	1.0327	0.1459	7.08	0.000
Ankle	0.2259	0.5417	0.42	0.678
Biceps	0.1483	0.2295	0.65	0.520
Wrist	−2.2034	0.8129	−2.71	0.008
S = 4.13552	R-Sq = 75.7%	R-Sq(adj) = 73.3%
Analysis of Variance
Source	DF	SS	MS	F	P
Regression	9	4807.36	534.15	31.23	0.000
Residual Error	90	1539.23	17.10
Total	99	6346.59

(a)  Interpret the coefficients of Age and Abdomen in context. Age is measured in years and Abdomen is abdomen circumference in centimeters.

(b)  Use the p-value from the ANOVA test to determine whether the model is effective.

(c)  Interpret R² in context.

(d)  Which explanatory variable is most significant in the model? Which is least significant?

(e)  Which variables are significant at a 5% level?

Answer 1