**Relationship Between Happiness Index and Life Expectancy: A Regression Analysis**A regression analysis was conducted to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).**Results of the Regression Analysis:**\[ \hat{y} = a + bx \]Where:- $ a = 0.137 $- $ b = 0.082 $This suggests that for every additional year of life expectancy, the happiness index is predicted to increase by 0.082 units, starting from a base level of 0.137 when life expectancy is zero.*(Note: There were no graphs or additional diagrams provided in the source image.)* ### Educational Portal: Statistical Analysis Exercises#### Question (d)If the life expectancy is increased by 3.5 years in a certain country, how much will the happiness index change? Round to two decimal places. [Answer Input Box]---#### Question (e)Use the regression line to predict the happiness index of a country with a life expectancy of 84 years. Round to two decimal places.[Answer Input Box]---**Explanation of Graphs and Diagrams (if applicable)**In this exercise, students are expected to understand and apply concepts of linear regression analysis. While there are no direct graphs or diagrams referenced in the questions, typically, such problems are solved using a regression line which represents the relationship between two variables—in this case, life expectancy and the happiness index.1. **Linear Regression Line**: A linear regression line is an equation in the form of $ y = mx + c $ where: - `y` is the dependent variable (happiness index). - `x` is the independent variable (life expectancy). - `m` is the slope of the line. - `c` is the y-intercept.2. **Change Calculation**: For Question (d), understand how to calculate the change in the happiness index by multiplying the slope of the regression line with the increase in life expectancy.3. **Prediction Using Regression Line**: For Question (e), substitute the given life expectancy value (84 years) into the regression line equation to predict the corresponding happiness index.Students are encouraged to review their course materials on linear regression and application problems to solve these questions effectively.

Given Regression equation is Y=a+bx where a=0.137 b=0.082 Therefore Y=0.137+0.082x

A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x). The results of the regression were: j=a+bx a=0.137 b=0.082

A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x). The results of the regression were: j=a+bx a=0.137 b=0.082

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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