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 = 83 + 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	116
7	10	119
8	10	123
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 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 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 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 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

Part a)

	Experience (X)	Sales (Y)	X * Y	X2	Ŷ	SSE =Σ(Y - Ŷ)2	SST = Σ(Yi - Y̅ )2	SSR = Σ( Ŷ - Y̅ )2
	1	80	80	1	87	49	961	576
	3	97	291	9	95	4	196	256
	4	102	408	16	99	9	81	144
	4	107	428	16	99	64	16	144
	6	103	618	36	107	16	64	16
	8	116	928	64	115	1	25	16
	10	119	1190	100	123	16	64	144
	10	123	1230	100	123	0	144	144
	11	127	1397	121	127	0	256	256
	13	136	1768	169	135	1	625	576
Total	70	1110	8338	632	3863.971	160	2432	2272

X̅ = Σ (Xi / n ) = 70/10 = 7
Y̅ = Σ (Yi / n ) = 1110/10 = 111

SST = Σ(Yi - Y̅ )2 =  2432
SSR = Σ( Ŷ - Y̅ )2  = 2272

SSE =Σ(Y - Ŷ)2 = 160

Part b)

r2 = SSR / SST = 0.934

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.

Part c)

r = √ r2 = 0.967