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Based on the data shown below, calculate the regression line (each value to one decimal place) ý = X y 11.15 10.9 11.55 11.4 13.65 12.4 14.35 14.5 14.75 13 13.85 12.6 13.65 14 15.3 2 1 2 6 7 8 9 10 11 3 4 5 12 1 Talm 13 T X +

Based on the data shown below, calculate the regression line (each value to one decimal place) ý = X y 11.15 10.9 11.55 11.4 13.65 12.4 14.35 14.5 14.75 13 13.85 12.6 13.65 14 15.3 2 1 2 6 7 8 9 10 11 3 4 5 12 1 Talm 13 T X +

MATLAB: An Introduction with Applications
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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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 \( b \).
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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