Question

# Consider the data. xi 1 2 3 4 5 yi 3 7 4 10 12 The...

Consider the data.

 xi yi 1 2 3 4 5 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(yiŷi)2,SST = Σ(yiy)2,and SSR = Σ(ŷiy)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.)

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

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