Question

Use the value of the linear correlation coefficient r to find the percentage of the total variation that can be explained by the linear relationship between the two variables. r = 0.234 (Your answer should be a percent rounded to two decimal places as needed.)

Answer 1

5.47% of the total variation between the two variables can be explained by the regression line.

Explanation:

Given :

R value = 0.234

The R value is the correlation Coefficient ; which gives the type and level of correlation between two variables.

However, to Obtian the percentage variation which can be explained by by the regression line, we have to obtain the Coefficient of determination, R².

R² value is Obtained by taking the squared of the correlation Coefficient

Hence,

R² = 0.234² = 0.054756

R² = 0.05476 * 100% = 5.4756%

Hence, R² = 5.48%

This is interpreted as ; 5.47% of the total variation between the two variables can be explained by the regression line.