MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![Based on the data shown below, calculate the regression line (each value to one decimal place).
\[ \hat{y} = \ \text{_} \ x + \ \text{_} \]
| x | y |
|----|-------|
| 1 | 11.15 |
| 2 | 10.9 |
| 3 | 11.55 |
| 4 | 11.4 |
| 5 | 13.65 |
| 6 | 12.4 |
| 7 | 14.35 |
| 8 | 14.5 |
| 9 | 14.75 |
| 10 | 13 |
| 11 | 13.85 |
| 12 | 12.6 |
| 13 | 13.65 |
| 14 | 15.3 |
To solve this, use the formula for the least squares regression line:
\[ \hat{y} = a + bx \]
where \( b \) is the slope and \( a \) is the y-intercept, calculated using:
\[ b = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} \]
\[ a = \frac{\sum y - b(\sum x)}{n} \]
Calculate \( \sum x \), \( \sum y \), \( \sum xy \), and \( \sum x^2 \) using the data provided, then substitute these into the formulas to find \( a \) and \( b \).](https://content.bartleby.com/qna-images/question/97b5df25-1667-438a-b46e-c2a0d1ae7c86/cc5f2e76-2278-4f13-b10a-cb267dbedbc7/lya71at_processed.jpeg)
Transcribed Image Text:Based on the data shown below, calculate the regression line (each value to one decimal place).
\[ \hat{y} = \ \text{_} \ x + \ \text{_} \]
| x | y |
|----|-------|
| 1 | 11.15 |
| 2 | 10.9 |
| 3 | 11.55 |
| 4 | 11.4 |
| 5 | 13.65 |
| 6 | 12.4 |
| 7 | 14.35 |
| 8 | 14.5 |
| 9 | 14.75 |
| 10 | 13 |
| 11 | 13.85 |
| 12 | 12.6 |
| 13 | 13.65 |
| 14 | 15.3 |
To solve this, use the formula for the least squares regression line:
\[ \hat{y} = a + bx \]
where \( b \) is the slope and \( a \) is the y-intercept, calculated using:
\[ b = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} \]
\[ a = \frac{\sum y - b(\sum x)}{n} \]
Calculate \( \sum x \), \( \sum y \), \( \sum xy \), and \( \sum x^2 \) using the data provided, then substitute these into the formulas to find \( a \) and \( b \).
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