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 ý = 81 + 4x. Salesperson Years of Experience Annual Sales ($1,000s) 1 107 103 101 119 8 9 10 10 11 13 123 127 136 (a) Compute SST, SSR, and SSE. SST = SSR = SSE = (b) Compute the coefficient of determination 2. (Round your answer to three decimal places.) 12 = 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 did not provide a good fit as a small 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 (c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)

Answer 1

y^=81+4*x is the regression equation

	x	y	(y^i)	(yi−yi^)	(yi−y^i)2	(y^i−y¯)2	(yi−y¯)2
	1	80	85	-5	25	576	841
	3	97	93	4	16	256	144
	4	97	97	0	0	144	144
	4	107	97	10	100	144	4
	6	103	105	-2	4	16	36
	8	101	113	-12	144	16	64
	10	119	121	-2	4	144	100
	10	123	121	2	4	144	196
	11	127	125	2	4	256	324
	13	136	133	3	9	576	729
Sum	70	1090			310	2272	2582
mean	7	109			SSE	SSR	SST

a) SST and SSR SSE

SST	2582
SSR	2272
SSE	310

B) r²=SSR/SST=2272/2582=0.88

C) Sample correlation coefficient =sqrt(r²)=0.938

#Sample correlation coefficient=0.938