"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?
13. r =- 0.450"

13. r =- 0.450"

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 for a set of data is R is equal to 0.910. What is the coefficient of determination? How much of the variation is explained, and how much is unexplained? Awesome. So it appears for this particular problem we're asked to solve for 3 separate answers. Our first answers we're asked to figure out what the coefficient of determination is. So that's our first answer. Our 2nd and 3rd answers is we're asked to solve for how much of the variation is explained and how much is unexplained. So now that we know what we're ultimately trying to solve for, our first step that we need to take in order to solve this problem is we need to calculate the coefficient of determination, which is R2. And R squared is equal to in this particular case, 0.910 to the power of 2, which when we plug that into our calculator, we will find that it's equal to 0.8281. Our second step now is we need to calculate the percentage. So we need to take our coefficient of determination, and we need to convert it to a percentage. So we need to take 0.8281, and we need to multiply it by 100. And when we do that, we will find that it's equal to 82.8. percent when we round to one decimal place, and this 82.8% is our explained variation, which I'll call EV for short, and that is one of our final answers we're ultimately trying to solve for. Let us also note that our coefficient of determination, we could say that it is approximately equal to 0.8. 28 when we round to 3 decimal places. Fantastic. And let's put a box around that because that is one of our final answers that we're trying to solve for. So so far we've already solved for 2 out of our 3 final answers that we need to solve for. So with that in mind, let us recall and note that the coefficient of determination tells us how much of the variation in the dependent variable Y. Can be explained by the independent variable X using the regression line. And we should also recall that the remaining variation is due to other factors not explained by the model itself, such as randomness, other variables, or noise. So with that in mind, our third and final step is we need to calculate the unexplained variation. And in order to do that, we need to take 100% minus 82.8%, which is equal to 17.2%, and this 17.2% is unexplained. Which I'll call it UN for short for unexplained, and that's it. That is our third and final answer. So to quickly recap our final answers to note what we've learned and we will determine that without a doubt our final answers are once again as follows. So the coefficient of determination is 0.828. And 82.8% is explained, and 17.2% is unexplained, and that's it. Those are our final three answers. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

"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?
13. r =- 0.450"

Key Concepts

Correlation Coefficient (r)

Coefficient of Determination (r^2)

Explained vs. Unexplained Variation

Watch next

"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?13. r =- 0.450"

Key Concepts

Correlation Coefficient (r)

Coefficient of Determination (r^2)

Explained vs. Unexplained Variation

Watch next

"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?
13. r =- 0.450"