Question

Consider the data.

xi	1	2	3	4	5
yi	4	7	6	10	13

The estimated regression equation for these data is

ŷ = 1.70 + 2.10x.

(a) Compute SSE, SST, and SSR using equations SSE = Σ(y_i − ŷ_i)², SST = Σ(y_i − y)², and SSR = Σ(ŷ_i − y)².

SSE=

SST=

SSR=

(b) Compute the coefficient of determination r².

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) Compute the sample correlation coefficient. (Round your answer to three decimal places.)

Answer 1

Ans:

	x	y	y'	(y-y')^2	(y-8)^2	(y'-8)^2
	1	4	3.8	0.04	16	17.64
	2	7	5.9	1.21	1	4.41
	3	6	8	4	4	0
	4	10	10.1	0.01	4	4.41
	5	13	12.2	0.64	25	17.64
Total		40		5.9	50	44.1
	y-bar=	8		SSE	SST	SSR

a)

SSE=5.9

SST=50

SSR=44.1

b)r^2=SSR/SST=44.1/50=0.882

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)r=sqrt(0.882)=0.939