Consider the data.
x_{i} |
1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
y_{i} |
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 r^{2}.
r^{2}=
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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