Question

4. A researcher built a model to predict an indicator of fitness using heart-rate (X1), weight (X2), height (X3) and age (X4) as predictors. The model was Y = 4 - 1.2 X1 -0.5 X2 +0.6 X3-0.2X4. The standard errors for X1, X2, X3, and X4 were 0.4, 0.3, 0.5, and 0.06 respectively. 1. If SSR=15500, R2 is 0.333 and F-stat is 5, complete the ANOVA table. 2. Which of these variables is statistically the most significant? Why?

Answer 1

Ans:

1)

R^2=0.333=SSR/SST

0.333=15500/SST

SST=46500

SS(error)=46500-15500=31000

df(regression)=4

MS(regression)=15500/4=3875

MS(error)=3875/5=775

df(error)=31000/775=40

Source	SS	df	MS	F
Regression	15500	4	3875	5.00
error	31000	40	775
Total	46500	44

2)

	coefficient	standard error	t	p-value
X1	-1.2	0.4	-3	0.0046
X2	-0.5	0.3	-1.667	0.1034
X3	0.6	0.5	1.2	0.2372
X4	-0.2	0.06	-3.333	0.0019

X₄ is most significant,as p-value is smallest.