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 = ?0.601 Part A Calculate the coefficient of determination. (Round to three decimal places as needed.) Part B What does this tell you about the explained variation of the data about the regression line? (Round to one decimal place as needed.) Part C About the unexplained variation? (What percentage of unexplained variation does the model have? Round to one decimal place as needed.)

Explanation / Answer

Answer

(A) we have r = -0.601

we know that the coefficient of determination = r^2

setting the r value, we get

coefficient of determination = (-0.601)^2 = 0.361 (rounded to three decimals)

(B) we got the coefficient of determination r^2 = 0.361 or 36.1%

So, this means that 36.1% variation in the dependent variable can be explained by the independent variable.

or we can say that 36.1 % of the variation of the data about the regression line can be explained.

(C) Percentage of unexplained variation = 100 - percent of explained variation = 100-36.1 = 63.9 %

so, the model has 63.9% unexplained variation of the data about the regression line.

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