Question

Consider the data.

xi	1	2	3	4	5
yi	3	7	4	10	12

The estimated regression equation for these data is

ŷ = 0.90 + 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 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)

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

Answer 1

Ans:

	x	y	y'	(y-y')^2	(y'-7.2)^2	(y-7.2)^2
	1	3	3	0	17.64	17.64
	2	7	5.1	3.61	4.41	0.04
	3	4	7.2	10.24	0.00	10.24
	4	10	9.3	0.49	4.41	7.84
	5	12	11.4	0.36	17.64	23.04
Total		36		14.7	44.1	58.8
		7.2		SSE	SSR	SST

a)

SSE=14.7

SSR=44.1

SST=58.8

b)

R^2=44.1/58.8=0.75

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)

sample correlation coefficient=sqrt(0.75)=0.866