2. Using the data above: a. Find ₂ if we run the regression without intercept. b. Show (x,y) is not on the regression line.
2. Using the data above: a. Find ₂ if we run the regression without intercept. b. Show (x,y) is not on the regression line.
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
Please solve question 2, thanks!
![### Expert Q&A
#### 1. Consider the following 4 observations:
a) Fill in the table:
| x | y | (x-x̄) | (y-ȳ) | C*D | C^2 | ŷ | error |
|----|----|--------|-------|-----|-----|------|-------|
| 1 | 6 | | | | | | |
| 2 | 4 | | | | | | |
| 3 | 12 | | | | | | |
| 4 | 10 | | | | | | |
- Σx =
- Σy =
- x̄ (mean x) =
- ȳ (mean y) =
b) Use the table above to find the best coefficients for the following regression:
\[ y = \beta_1 + \beta_2 \cdot x \]
- (i.e. Find \(\beta_1\) and \(\beta_2\)).
c) Interpret the \(\beta\)s.
#### Part b:
c) Plot the data and the estimated linear regression (on the same graph).
d) Obtain the residuals for each observation and show that \(\sum_i e_i\) is indeed zero.
#### 2. Using the data above:
a) Find \(\beta_2\) if we run the regression without intercept.
b) Show \((\overline{X}, \overline{Y})\) is not on the regression line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2Fd85765eb-f06f-4748-b50e-393624037177%2F0v3lo7s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Expert Q&A
#### 1. Consider the following 4 observations:
a) Fill in the table:
| x | y | (x-x̄) | (y-ȳ) | C*D | C^2 | ŷ | error |
|----|----|--------|-------|-----|-----|------|-------|
| 1 | 6 | | | | | | |
| 2 | 4 | | | | | | |
| 3 | 12 | | | | | | |
| 4 | 10 | | | | | | |
- Σx =
- Σy =
- x̄ (mean x) =
- ȳ (mean y) =
b) Use the table above to find the best coefficients for the following regression:
\[ y = \beta_1 + \beta_2 \cdot x \]
- (i.e. Find \(\beta_1\) and \(\beta_2\)).
c) Interpret the \(\beta\)s.
#### Part b:
c) Plot the data and the estimated linear regression (on the same graph).
d) Obtain the residuals for each observation and show that \(\sum_i e_i\) is indeed zero.
#### 2. Using the data above:
a) Find \(\beta_2\) if we run the regression without intercept.
b) Show \((\overline{X}, \overline{Y})\) is not on the regression line.
Expert Solution
Step 1
The given regression line is,
................(I)
Here, is the intercept and is the slope.
The regression line without intercept is obtained by substituting = 0 in the above equation(I)
The slope equation is obtained by using the formula,
Step by step
Solved in 3 steps with 4 images
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