### Bivariate Data Analysis#### Data SetWe have a bivariate data set represented in the table below with variables \( x \) and \( y \).| x | y ||------|------|| 45.6 | 79.6 || 74.1 | 49.0 || 51.8 | 80.3 || 50.4 | 67.9 || 49.2 | 83.3 || 55.9 | 66.4 || 42.1 | 92.7 || 39.5 | 84.3 || 96.3 | 28.6 |#### Instructions1. **Correlation Coefficient:** Calculate the correlation coefficient (\( r \)) and report it to three decimal places. \[ r = \_\_\_\_\_ \]2. **Proportion of Variation Explained ( \( R^2 \)):** Calculate the proportion of the variation in \( y \) that can be explained by the variation in the values of \( x \). Report the answer as a percentage accurate to one decimal place. \[ R^2 = \_\_\_\_\_ \% \]### Detailed Explanation of Concepts1. **Correlation Coefficient ( \( r \) ):** - The correlation coefficient measures the strength and direction of the linear relationship between two quantitative variables. - It ranges from -1 to 1, where: - 1 indicates a perfect positive linear relationship, - -1 indicates a perfect negative linear relationship, - 0 indicates no linear relationship.2. **Coefficient of Determination ( \( R^2 \) ):** - The \( R^2 \) value, also known as the coefficient of determination, represents the proportion of the variance in the dependent variable (\( y \)) that can be explained by the independent variable (\( x \)). - It is calculated as the square of the correlation coefficient (\( r^2 \)) and expressed as a percentage. - For example, an \( R^2 \) value of 0.64 (or 64%) indicates that 64% of the variance in \( y \) can be explained by the variance in \( x \).Complete the calculations to find the values of \( r \) and \( R^2 \) as per the instructions provided

Name: ### Bivariate Data Analysis#### Data SetWe have a bivariate data set
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Description: ### Bivariate Data Analysis#### Data SetWe have a bivariate data set represented in the table below with variables \( x \) and \( y \).| x | y ||------|------|| 45.6 | 79.6 || 74.1 | 49.0 || 51.8 | 80.3 || 50.4 | 67.9 || 49.2 | 83.3 || 55.9 |

Math

Statistics

Here is a bivariate data set. y 45.6 79.6 74.1 49 51.8 80.3 50.4 67.9 49.2 83.3 55.9 66.4 42.1 92.7 39.5 84.3 96.3 28.6 Find the correlation coefficient and report it accurate to three decimal places. r = What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. R2 =

Here is a bivariate data set. y 45.6 79.6 74.1 49 51.8 80.3 50.4 67.9 49.2 83.3 55.9 66.4 42.1 92.7 39.5 84.3 96.3 28.6 Find the correlation coefficient and report it accurate to three decimal places. r = What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. R2 =

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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