Question

The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,803 and 1,756, respectively.
(a) Compute R2. (Round your answer to three decimal places.) R2 =
(b) Compute Ra2. (Round your answer to three decimal places.) Ra2 =
(c) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)
The estimated regression equation provided a good fit as a large proportion of the variability in y has been explained by the estimated regression equation.
The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.
The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.
The estimated regression equation did not provide a good fit as a large proportion of the variability in y has been explained by the estimated regression equation.

Answer 1

Answer:

a) = 0.9739

b) = 0.969

c) option A is correct

Step-by-step explanation:

Given that:

sample size n = 30

SST = 1803

SSR = 1756

$R^2 = \dfrac{SSR}{SST} \\ \\ R ^2 = \dfrac{1756}{1803} \\ \\ \mathbf{R^2 =0.9739}$

The adjusted $R_a^2$ is computed as:

$R_a^2 = 1 - (\dfrac{n-1}{n-p})(1-R^2)$

where;

$p = k+1 \\ p= 4+1 = 5$

$R_a^2 = 1 - (\dfrac{30-1}{30-5})(1-0.9739)$

$R_a^2 = 1 - (\dfrac{29}{25})(0.0261)$

$R_a^2 = 1 - (1.16)(0.0261)$

$R_a^2 = 1 -0.030276$

$\mathbf{R_a^2 \simeq 0.969}$