Question

Consider the data.

xi	3	12	6	20	14
yi	65	35	50	15	20

The estimated regression equation for these data is

ŷ = 70 − 3x.

(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.)

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 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 provided 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 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.

(c)

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

Answer 1

The statistical software output for this problem is :

SSE = 110

SST = 1730

SSR = 1620

r ² = 0.936

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.

sample correlation coefficient = r = -0.968