Question

A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is

ŷ = 82 + 4x.

Salesperson	Years of Experience	Annual Sales ($1,000s)
1	1	80
2	3	97
3	4	102
4	4	107
5	6	103
6	8	101
7	10	119
8	10	128
9	11	127
10	13	136

(a)

Compute SST, SSR, and SSE.

SST = SSR = SSE =

(b)

Compute the coefficient of determination

r².

(Round your answer to three decimal places.)

r²

=

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.     The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.

(c)

What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)

Answer 1

Since the regression equatiin

Y = 82+4x

a) SSR = 2272

SSE = 370

SST = 2642

b) coefficient of determination

R^2 = SSR/SST

= 2272/2642= 0.860

The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.

d) sample correlation coefficient

r = 0.927

ANOVA table

Source	DF	Sum of Square	Mean Square	F Statistic	P-value
Regression (between ŷiand yi)	1	2272.000000	2272.000000	49.124324	0.000111646
Residual (between yiand ŷi)	8	370.000000	46.250000
Total(between yiand yi)	9	2642.000000	293.555556

	Coeff	SE	t-stat	lower t0.025(8)	upper t0.975(8)	Stand Coeff	p-value	VIF
b	82.000000	4.537015	18.073556	71.537624	92.462376	0.00000	9.01638e-8
X1	4.000000	0.570705	7.008875	2.683952	5.316048	0.927337