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  3. consider the data. xi 3 12 6 20 14 yi 65

Consider the data. xi 3 12 6 20 14 yi 65 40 60 15 20 The estimated regression equation for these data is ŷ = 75.75 − 3.25x. (a) Compute SSE,...

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Question

Statistics

Consider the data.

xi

31262014

yi

6540601520

The estimated regression equation for these data is

ŷ = 75.75 − 3.25x.

(a)

Compute SSE, SST, and SSR using equations

SSE = Σ(yi −ŷi)2,

SST = Σ(yi −y)2,

and

SSR = Σ(ŷi −y)2.

SSE = SST = SSR =

(b)

Compute the coefficient of determination

r2.

(Round your answer to three decimal places.)

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 largeproportion of the variability in y has been explained bythe least squares line.The least squares line provided a good fitas a large proportion of the variability in y has beenexplained by the least squaresline.     The least squares line did notprovide a good fit as a small proportion of the variability iny has been explained by the least squares line.The leastsquares line provided a good fit as a small proportion of thevariability in y has been explained by the least squaresline.

(c)

Compute the sample correlation coefficient. (Round your answerto three decimal places.)

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