Use the value of the linear correlation coefficient to calculate the coefficient

Question

Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

r = 0.501

Calculate the coefficient of determination.

(Round to three decimal places as needed.)

What does this tell you about the explained variation of the data about the regression line?

% of the variation can be explained by the regression line.

(Round to one decimal place as needed.)

About the unexplained variation?

% of the variation is unexplained and is due to other factors or to sampling error.

(Round to one decimal place as needed.)

Explanation / Answer

we are given the correlation as r = 0.501 , so the r square value is (0.501)^2 = 0.251

What does this tell you about the explained variation of the data about the regression line?

this value tells us that the percentage of variation explained by the model or regression line is 25.1%

About the unexplained variation?

so , about (100-25.1)= 74.89% variation in the data is not explained or captured by the model

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