Consider a Qunat vars X and Y and suppose we have collected data on both of them from an underlying population: X1, X2,...,xn У1.У...... Уп PowerPoint Slide Show-LinearReg.pptx-PowerPoint Bivariate Analysis: Modelling a Linear Relation XY After checking their scatter graph and correlation, if the amount of linear relation between the two was high enough, we can model the relation using a linear function: Y=f(X)=a+bX To that end, we need to estimate a and b. b= nΣ(xy) - ExΣy nEx - (Σ»)? a= Σy-bΣx n Ex: Linear of Model of Whr and Salary. Oba Whrs X 1 6 2 8 9 9 10 9 8 7 6 3 4 5 6 8 9 10 7 Salary Y 8 20 30 35 50 38 25 23 15 26 48 160 970 315 500 342 200 161 90 182 X^2 36 64 81 81 100 81 64 49 36 49 MULTIPLE CHOICE QUESTION The Cor(X,Y)=0.9, hence b in Y=a+bX is negative negative positive Rewatch Submit
Consider a Qunat vars X and Y and suppose we have collected data on both of them from an underlying population: X1, X2,...,xn У1.У...... Уп PowerPoint Slide Show-LinearReg.pptx-PowerPoint Bivariate Analysis: Modelling a Linear Relation XY After checking their scatter graph and correlation, if the amount of linear relation between the two was high enough, we can model the relation using a linear function: Y=f(X)=a+bX To that end, we need to estimate a and b. b= nΣ(xy) - ExΣy nEx - (Σ»)? a= Σy-bΣx n Ex: Linear of Model of Whr and Salary. Oba Whrs X 1 6 2 8 9 9 10 9 8 7 6 3 4 5 6 8 9 10 7 Salary Y 8 20 30 35 50 38 25 23 15 26 48 160 970 315 500 342 200 161 90 182 X^2 36 64 81 81 100 81 64 49 36 49 MULTIPLE CHOICE QUESTION The Cor(X,Y)=0.9, hence b in Y=a+bX is negative negative positive Rewatch Submit
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Bivariate Analysis: Modelling a Linear Relation**
Consider a Quantitative Variables X and Y and suppose we have collected data on both of them from an underlying population:
\( x_1, x_2, ..., x_n \)
\( y_1, y_2, ..., y_n \)
After checking their scatter graph and correlation, if the amount of linear relation between the two was high enough, we can model the relation using a linear function: \( Y=f(X)=a+bX \)
To that end, we need to estimate \( a \) and \( b \).
\[ b = \frac{n\sum(xy) - \sum x \sum y}{n\sum x^2 - (\sum x)^2} \]
\[ a = \frac{\sum y - b\sum x}{n} \]
**Example: Linear Model of Whr and Salary.**
| Obs | X (Whr) | Y (Salary) | XY | X\(^2\) |
|-----|---------|------------|-----|---------|
| 1 | 6 | 8 | 48 | 36 |
| 2 | 9 | 20 | 160 | 64 |
| 3 | 9 | 30 | 270 | 81 |
| 4 | 9 | 35 | 315 | 81 |
| 5 | 10 | 50 | 500 | 100 |
| 6 | 7 | 50 | 342 | 49 |
| 7 | 9 | 8 | 72 | 81 |
| 8 | 7 | 23 | 161 | 49 |
| 9 | 6 | 7 | 42 | 36 |
| 10 | 7 | 26 | 182 | 49 |
**Multiple Choice Question**
The Cor(X,Y)=0.9, hence b in Y=a+bX is:
- [ ] negative
- [ ] positive
**Explanation of Graph**
The table presents the observed data points with variables X (Whr) and Y (Salary), along with the calculated products \( XY \) and squares \( X^2 \) for each](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffaba5c86-73f4-4934-9afb-0b245e418cf2%2Fd591269f-1da3-4fb3-a76d-9848fbaa7a75%2F6t7r1e5r_processed.png&w=3840&q=75)
Transcribed Image Text:**Bivariate Analysis: Modelling a Linear Relation**
Consider a Quantitative Variables X and Y and suppose we have collected data on both of them from an underlying population:
\( x_1, x_2, ..., x_n \)
\( y_1, y_2, ..., y_n \)
After checking their scatter graph and correlation, if the amount of linear relation between the two was high enough, we can model the relation using a linear function: \( Y=f(X)=a+bX \)
To that end, we need to estimate \( a \) and \( b \).
\[ b = \frac{n\sum(xy) - \sum x \sum y}{n\sum x^2 - (\sum x)^2} \]
\[ a = \frac{\sum y - b\sum x}{n} \]
**Example: Linear Model of Whr and Salary.**
| Obs | X (Whr) | Y (Salary) | XY | X\(^2\) |
|-----|---------|------------|-----|---------|
| 1 | 6 | 8 | 48 | 36 |
| 2 | 9 | 20 | 160 | 64 |
| 3 | 9 | 30 | 270 | 81 |
| 4 | 9 | 35 | 315 | 81 |
| 5 | 10 | 50 | 500 | 100 |
| 6 | 7 | 50 | 342 | 49 |
| 7 | 9 | 8 | 72 | 81 |
| 8 | 7 | 23 | 161 | 49 |
| 9 | 6 | 7 | 42 | 36 |
| 10 | 7 | 26 | 182 | 49 |
**Multiple Choice Question**
The Cor(X,Y)=0.9, hence b in Y=a+bX is:
- [ ] negative
- [ ] positive
**Explanation of Graph**
The table presents the observed data points with variables X (Whr) and Y (Salary), along with the calculated products \( XY \) and squares \( X^2 \) for each
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