Answered: Consider the data. xi 3 12 6 20 14 yi…

Elementary Linear Algebra (MindTap Course List)

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Question

Consider the data.

x_i	3	12	6	20	14
y_i	55	35	60	15	25

The estimated regression equation for these data is

ŷ = 68.25 − 2.75x.

(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

r².

(Round your answer to three decimal places.)

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 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 large 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.)

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Consider the data. xi 3 12 6 20 14 yi 55 35 60 15 25 The estimated regression equation for these data is ŷ = 68.25 − 2.75x. (a) Compute SSE, SST, and SSR using equations SSE = Σ(yi − ŷi)2, SST = Σ(yi − y)2, and SSR = Σ(ŷi − y)2.