Question

Calculate the linear regression equation for each of these situations:

1. Variable X: range = 0-60, Xi = 45, s(x) = 5

Variable Y: range = 0 -25, Ybar = 11, s(y) = 3

Correlation: r = .30

2. Variable X: range = 0-100, Xi = 37.22, s(x) = 11.76

Variable Y: range = 0 -150, Ybar = 104.32, s(y) = 15.92

Correlation: r = .62

3. Variable X: range = 1-6, Xi = 4.32, s(x) = .97

Variable Y: range = 1-5, Ybar = 2.51, s(y) = .46

Correlation: r = -0.09

4. Variable X: range = 1-5, Xi = 3.91, s(x) = 1.04

Variable Y: range = 1-110, Ybar = 76.40, s(y) = 9.87

Correlation: r = .25

Answer 1

1)

	x̅ =		45
	y̅ =		11
	sx=		5
	sy =		3
	r=		0.3
slope b1=r*sy/sx=			0.180
intercept bo=y̅ +r(sy/sx)*(x̅)=			2.900

line equation: Yhat =2.9+0.18*x

2)

	x̅ =		37.22
	y̅ =		104.32
	sx=		11.76
	sy =		15.92
	r=		0.62
slope b1=r*sy/sx=			0.839
intercept bo=y̅ +r(sy/sx)*(x̅)=			73.081

line equation: Yhat =73.081+0.839*x

3)

slope b1=r*sy/sx=			-0.043
intercept bo=y̅ +r(sy/sx)*(x̅)=			2.694

line equation: Yhat =2.694-0.043x

4)

slope b1=r*sy/sx=			2.373
intercept bo=y̅ +r(sy/sx)*(x̅)=			67.123

line equation: Yhat =67.123+2.373x