## Finding the Equation of the Least-Squares Regression Line**Given Data:**- $ x $ values: -5, -3, 4, 1, -1, -2, 0, 2, 3, -4- $ y $ values: 11, -6, 8, -3, -2, 1, 5, -5, 6, 7**Task:** Find the equation of the least-squares regression line for the given data. Round values to three decimal places.**Options:**A. $ \hat{y} = 0.206x - 2.097 $B. $ \hat{y} = 2.097x - 0.206 $C. $ \hat{y} = -2.097x + 0.206 $D. $ \hat{y} = -0.206x + 2.097 $**Correct Answer:**- The selected answer is option B: $ \hat{y} = 2.097x - 0.206 $### Explanation:The least-squares regression line is used to predict the relationship between the independent variable $ x $ and the dependent variable $ y $. It minimizes the sum of the squares of the residuals (the differences between the observed and predicted $ y $ values). The equation is in the form $ \hat{y} = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. In this scenario, the slope is approximately 2.097, and the y-intercept is approximately -0.206.

Answered: Find the equation of the least-squares…

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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Find the equation of the least-squares regression line for the given data. Round values to three decimal places. -5 -3 11 -6 X y OA.y=0.206x-2.097 OB. y=2.097x-0.206 C. y = -2.097x+ 0.206 D. y=-0.206x + 2.097 4 1 8 -3 -1 -2 -2 1 05 2 -5 3 6 -41 7