**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.

Answered: Image /qna-images/answer/c9704049-014d-477b-87a2-e280211f62db.jpg

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

See similar textbooks

Similar questions

Use the scatterplot of Vehicle Registrations below to answer the questions Vehicle Registrations in the United States, 1925- 2011 Vehicles millions 300 y = 3.0161x - 5819.5 R? = 0.9695 250 200 150 100 50 1920 -50 1940 1960 1980 2000 2020 Year Write a sentence explaining the value of the slope for this regression line. For every increase in year, the number of vehicle registrations in the US increases by 3.0161 million. For every increase in year, the number of vehicle registrations in the US increases by 5819.5. For every increase in vehicle registrations in the US, the number of years increases by 5819.5. For every increase in vehicle registrations in the US, the number of years increases by 3.0161 million. Registrations (in millions)
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 = ___ x + ____ x y 4 12.52 5 14.4 6 12.58 7 17.06 8 18.04 9 18.22 10 20.4 11 23.78 12 23.36
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 40 inches. Is the result close to the actual weight of 352 pounds? Use a significance level of 0.05. Chest size (inches) *Weight (pounds) 44 54 328 528 41 55 39 51 418 580 296 503 Click the icon to view the critical values of the Pearson correlation coefficient r. - What is the regression equation? x (Round to one decimal place as needed.)
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 D 2. 19.44 3. 19.8 4 16.96 16.42 6. 14.78 7 14.94 8. 12.5
Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Assume that temperature is independent each year. Based on the data shown below, calculate the regression line (each value to two decimal places). First the slope and then the y-intercept. Y X 3 4 5 67 8 00 a 9 y 10.14 10.85 11.86 11.17 7.58 9.79 7.5 x+
Annual high temperatures in a certain location have been tracked for several years. Let XX represent the year and YY the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).y = ___ x + ____ x y 3 11.49 4 10.82 5 11.05 6 13.58 7 13.51 8 17.04 9 18.27 10 19.6
Run a regression analysis on the following data set, where y is the final grade in a math class and x is the average number of hours the student spent working on math each week. hours/week Grade y 8. 72.2 8. 58.2 10 60 11 71.4 14 92.6 14 76.6 14 75.6 14 83.6 15 81 20 100 State the regression equation with constants accurate to 2 decimal places. ý = What is the predicted value for the final grade when a student spends an average of 15 hours each week on math? Round to 2 decimal places. Question Help: D Video 1 Video 2 Submit Question
Annual high temperatures in a certain location have been tracked for several years. Let Xrepresent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).y = x + x y 5 25.45 6 25.48 7 30.41 8 33.84 9 36.27 10 36.7 11 42.13 12 45.86 13 46.49 14 50.42 15 52.75 16 57.58 17 57.81 18 62.44
Perform a linear regression analysis on the following data and determine the "a" coefficient (i.e., slope): Y 4.99 22.19 1.96 9.89 2.98 11 9 40.46 4.04 18.93 6.06 25 0.88 0.19 8.02 34.02 6.97 28.03
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value? Chirps in 1 min 1118 796 1161 918 1103 1219 Temperature (F) 82 72.2 92.2 73 87.5 94.4