calculate r-squared,--the coefficient of determination--given that the linear correlation coefficient, r, is -0.187. what does this tell you about the explained variation and the unexplained variation of the data about the regression line?



Answer :

The value of r-squared (the coefficient of determination) is 0.035. It tells us that 3.5% explained variation and 96.5% of the variation is unexplained.

What is r-squared?

R-squared (R²) is a statistical measure of the proportion of the dependent variable's variance explained by one or more independent variables in a regression model. Correlation describes the strength of the relationship between the independent and dependent variables, while r-squared describes how much the variance of one variable explains the variance of the second variable. Formula for R-Squared is

R² = 1 - Unexpected variation/total variation

We have , Linear correlation coefficient, r = -0.187

Coefficient of determination, r² = (-0.187)²

= 0.035

This value tells us the proportion of variation in the dependent variables that is explained by the independent variable. The coefficient of determination, R² = 0.035. That is 3.5% of the variation is explained and 96.5% of the variation is unexplained.

To learn more about R-squared, refer :

https://brainly.com/question/17031457

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