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.)

a)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.

b)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.   

c) 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) 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

The statistical software output for this problem is :

(a)

SSE = 14.7

SST = 58.8

SSR = 44.1

(b)

r ² = 0.75

c) 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 = 0.866