The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x, - 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,809 and 1,757, respectively.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
The following estimated regression equation based on 30 observations was presented.

\[
\hat{y} = 17.6 + 3.8x_1 - 2.3x_2 + 7.6x_3 + 2.7x_4
\]

The values of SST and SSR are 1,809 and 1,757, respectively.

(a) Compute \( R^2 \). (Round your answer to three decimal places.)

\( R^2 = \) [ ]

(b) Compute \( R_a^2 \). (Round your answer to three decimal places.)

\( R_a^2 = \) [ ]

(c) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

- \( \circ \) 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.
- \( \circ \) 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.
- \( \circ \) 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.
- \( \circ \) 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.
Transcribed Image Text:The following estimated regression equation based on 30 observations was presented. \[ \hat{y} = 17.6 + 3.8x_1 - 2.3x_2 + 7.6x_3 + 2.7x_4 \] The values of SST and SSR are 1,809 and 1,757, respectively. (a) Compute \( R^2 \). (Round your answer to three decimal places.) \( R^2 = \) [ ] (b) Compute \( R_a^2 \). (Round your answer to three decimal places.) \( R_a^2 = \) [ ] (c) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) - \( \circ \) 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. - \( \circ \) 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. - \( \circ \) 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. - \( \circ \) 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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman