Question

Consider the data. xi 1 2 3 4 5 yi 4 7 6 10 13 The...

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(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.)

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.)

Homework Answers

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

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