Consider the data. x₁ 1 2 3 4 Y₁ 4 7 5 4 12 15 The estimated regression equation for these data is ŷ = 0.30 + 2.70x. (a) Compute SSE, SST, and SSR using equations SSE = (y₁ - y)², SST = (y₁ - y)², and SSR = (₁ - y)². SSE = SST = SSR = (b) Compute the coefficient of determination ². 2²= Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O 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. O 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 provided a good fit as a large proportion of the variability in y has been explained by the least squares line. O 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) Compute the sample correlation coefficient. (Round your answer to three decimal places.)
Consider the data. x₁ 1 2 3 4 Y₁ 4 7 5 4 12 15 The estimated regression equation for these data is ŷ = 0.30 + 2.70x. (a) Compute SSE, SST, and SSR using equations SSE = (y₁ - y)², SST = (y₁ - y)², and SSR = (₁ - y)². SSE = SST = SSR = (b) Compute the coefficient of determination ². 2²= Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O 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. O 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 provided a good fit as a large proportion of the variability in y has been explained by the least squares line. O 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) Compute the sample correlation coefficient. (Round your answer to three decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Need the steps as well on how to solve, please.
![### Regression Analysis and Coefficient of Determination
Consider the data set below.
| \( x_i \) | 1 | 2 | 3 | 4 | 5 |
|-----------|---|---|---|---|---|
| \( y_i \) | 4 | 7 | 4 | 12 | 15 |
The estimated regression equation for these data is \( \hat{y} = 0.30 + 2.70x \).
#### (a) Compute SSE, SST, and SSR
Using the equations:
- SSE (Sum of Squared Errors): \( \Sigma (y_i - \hat{y})^2 \)
- SST (Total Sum of Squares): \( \Sigma (y_i - \bar{y})^2 \)
- SSR (Regression Sum of Squares): \( \Sigma (\hat{y} - \bar{y})^2 \)
- SSE = [Blank for student input]
- SST = [Blank for student input]
- SSR = [Blank for student input]
#### (b) Compute the coefficient of determination \( r^2 \)
The coefficient of determination is calculated as:
\[ r^2 = [Blank for student input] \]
**Comment on the goodness of fit.** (Consider a proportion large if it is at least 0.55.)
- \( \circ \) 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.
- \( \circ \) 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.
- \( \bullet \) 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.
- \( \circ \) 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) Compute the sample correlation coefficient.
Round your answer to three decimal places:
- [Blank for student input]
This exercise helps in understanding how to evaluate the quality of a regression model using various statistical measures and graphical interpretations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2fdea76-24b5-4e92-ab93-0d275ab88ec3%2F3a5788c2-9b6f-4818-96db-1836c1f4d2fa%2Fw271bq_processed.png&w=3840&q=75)
Transcribed Image Text:### Regression Analysis and Coefficient of Determination
Consider the data set below.
| \( x_i \) | 1 | 2 | 3 | 4 | 5 |
|-----------|---|---|---|---|---|
| \( y_i \) | 4 | 7 | 4 | 12 | 15 |
The estimated regression equation for these data is \( \hat{y} = 0.30 + 2.70x \).
#### (a) Compute SSE, SST, and SSR
Using the equations:
- SSE (Sum of Squared Errors): \( \Sigma (y_i - \hat{y})^2 \)
- SST (Total Sum of Squares): \( \Sigma (y_i - \bar{y})^2 \)
- SSR (Regression Sum of Squares): \( \Sigma (\hat{y} - \bar{y})^2 \)
- SSE = [Blank for student input]
- SST = [Blank for student input]
- SSR = [Blank for student input]
#### (b) Compute the coefficient of determination \( r^2 \)
The coefficient of determination is calculated as:
\[ r^2 = [Blank for student input] \]
**Comment on the goodness of fit.** (Consider a proportion large if it is at least 0.55.)
- \( \circ \) 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.
- \( \circ \) 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.
- \( \bullet \) 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.
- \( \circ \) 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) Compute the sample correlation coefficient.
Round your answer to three decimal places:
- [Blank for student input]
This exercise helps in understanding how to evaluate the quality of a regression model using various statistical measures and graphical interpretations.
Expert Solution
Step 1: Introduction
Correlation: The statistical relationship between two variables is known as correlation. The square of sample correlation coefficient known as Coefficient of determination.
The answer is attached below.
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman