**Understanding Linear Regression through Temperature Data**On this educational webpage, we aim to delve into the concept of linear regression using a practical example. Consider the scenario where annual high temperatures in a specific location have been tracked over several years. Here’s how you can calculate the regression line using the given data.Let \( X \) represent the year, and \( Y \) represent the high temperature. The data presented below outlines \( X \) and \( Y \) values:| \( x \) | \( y \) ||:------:|:-------:|| 2 | 19.56 || 3 | 20.25 || 4 | 17.14 || 5 | 18.13 || 6 | 16.82 || 7 | 15.11 || 8 | 10.2 |To determine the regression line, we use the equation:\[ y = mx + b \]Where:- \( m \) is the slope of the line.- \( b \) is the y-intercept.**Steps to Calculate the Regression Line:**1. Calculate the means of \( x \) and \( y \).2. Find the slope (\( m \)) using the formula: \[ m = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}} \]3. Determine the y-intercept (\( b \)) using the formula: \[ b = \bar{y} - m\bar{x} \]By plugging in the given data values to these formulas, you can compute the exact slope and intercept, hence determining the final equation for the regression line. Once computed, you can fill in the blanks in the following format:\[ y = \text{(slope\_value)} x + \text{(intercept\_value)} \]This approach will help you better understand the relationship between the years and the high temperatures recorded in this location, and how to interpret the trends represented in the regression model.

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Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). y = y 19.56 20.25 4 17.14 5 18.13 16.82 7 15.11 8 10.2

Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). y = y 19.56 20.25 4 17.14 5 18.13 16.82 7 15.11 8 10.2

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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