"In Exercises 7-10, use the value of the correlation coefficie...

Question

"In Exercises 7-10, 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?
7. r =0.465"

7. r =0.465"

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Suppose the correlation coefficient between two variables is R equals 0.732. What is the coefficient of determination R2? What percentage of the variation in the data is explained by the regression line, and what percentage is unexplained? Awesome. So it appears for this particular problem we're asked to solve for three separate answers based on the information that is provided to us by the problem itself. So our first answer is we're asked to determine what the value for the coefficient of determination R squared is. We're trying to solve for R2d. That is our first answer. Our second answer is we're asked to determine what the percentage is for the variation in the data that is explained by the regression line. That's our second answer. And we're also asking to determine what percentage of the variation in data is unexplained by the regression line, and that's our third and final answer we are ultimately trying to solve for. So now that we know what we're trying to solve for, let's read off our multiple choice answers to see what our final answer set might be, noting that all of them state an answer for R2d equals some value first. Then they have a a percentage for both the explained and unexplained, and I'll read them. Order and noting once again that the explained and unexplained values are both percentages. So A is 0.536 and 46.4 and 53.6. B is 0.536 and 53.6 and 46.4. C is 0.464 and 53.6 and 46.4. And finally, D is 0.536 and 52.9 and 47.1. Awesome. So our first step that we need to take in order to solve this particular problem is we need to square the correlation coefficient. So we need to note that R2 is equal to 0.732 to 2, which is approximately equal to 0.536 when we round to three decimal places. And that is our first answer that we are trying to solve for. Hooray, we did it. Our second step now is we need to determine the explained variation. And the explained variation is 0.536, or when we convert our decimal to a percentage, we will get 53.6%. So all we have to do is just take 0.536 and we multiply it by 100 in order to get our final answer for the explained variation, which once again is 53.6%. So that's our second answer. Now solving for our 3rd and final answer, we need to determine the unexplained variation. And as we should recall, in order to determine the unexplained variation, we need to take 1 minus 0. 536, which is equal to 0.464, which once again multiplying this value by 100 to convert our decimal to a percentage, we will get a percentage of 46.4%, and this is our final answer for the unexplained variation, which I'll call UE for unexplained. And our 53.6% is for our explained variation, which I'll just simply call E in quotation marks. So looking at our multiple choice answers, the correct answer will have to be multiple choice answer letter B, which once again is R squared is equal to 0. 536. Explained is 53.6% and unexplained is 46.4%. And that's it. That is our final answer or answers, I should say. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

"In Exercises 7-10, 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?7. r =0.465"

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"In Exercises 7-10, 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?
7. r =0.465"