Consider the data.
xi
1
2
3
4
5
yi
4
7
4
12
15
The estimated regression equation for these data is
ŷ = 0.30 + 2.70x.
(a)
Compute SSE, SST, and SSR using equations
SSE = Σ(yi − ŷi)²,
SST = Σ(yi − ȳ)²;
and
SSR = Σ(ŷi − ȳ)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.)