"In Exercises 13-16, use the value of the correlation coeffici...

Question

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?
16. r = 0.795"

16. r = 0.795"

Accepted Answer

All right, hello, everyone. So, this question says, if the correlation coefficient for a data set is R equals -0.57, what is the coefficient of determination R squared? How much of the variation is explained by the regression line and how much is unexplained? All right, so first, let's begin with our. Coefficient of determination, which is the square of the correlation coefficient. So here are squared. Is equal to -0.57 to the second power. Which gives you 0.3249. So R squared essentially gives you the. Variation that's explained by the regression line, and you find this specifically by multiplying R2 by 100 to get you a percentage. So, 0.3249 multiplied by 100. Gives you 32.49%. As the explained variation. So to find the unexplained variation, you would subtract your explained from 100%, or You can subtract 0. 3249 from 1. This gives you 0.6751. Which equals 67.51%. So ultimately Now we can summarize our final answer. First, R squared, if you recall, was equal to 0.3249. And so the explained variation routed to one decimal place is 32.5%. And the unexplained variation is 67.5%, again rounded to one decimal place. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?16. r = 0.795"

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"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?
16. r = 0.795"