Question

Consider the data.

xi	3	12	6	20	14
yi	60	35	55	15	15

The estimated regression equation for these data is

ŷ = 69 − 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 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.

-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.

(c)

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

Answer 1

The statistical software output for this problem is :

SSE=200

SST= 1820

SSR= 1620

r² = 0.890

-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)

sample correlation coefficient = -0.943