"Old Vehicles In Exercises 31–34, use the figure shown at the ...

Question

"Old Vehicles In Exercises 31–34, use the figure shown at the left.

33. Coefficient of Determination Find the coefficient of determination r^2 and interpret the results."

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 advertising expenditure and product sales is R equals 0.59, what is the coefficient of determination R squared, and how should it be interpreted? Awesome. So it appears for this particular problem based on all the information that is provided to us, we're asked to determine what is the coefficient of determination value R squad, and that's our first answer, and our second answer is how should this coefficient of determination be interpreted? So how should this be interpreted? That's our second answer. So with that in mind, now that we know that we're ultimately trying to solve for two separate answers, let us read off our multiple choice answers to see what our final answer pair might be. A is 0.35, 35% of the variation in product sales is explained by advertising expenditure. B is 0.41% and 41% of the variation in product sales is explained by advertising expenditure. C is 0.59 and 59% of the variation in product sales is explained by advertising expenditure, and finally, D is 0.28% and 28% of the variation in product sales is explained by advertising expenditure. OK, so our first step in order to solve this particular problem is we need to solve for our coefficient of determination. So we need to square the correlation coefficient. So R squared is equal to 0.59, once again noting that we're told that R is equal to 0.59. So we need to take 0.59 and we need to square it, and when we do, we will find that it's equal to 0.3481. Fantastic. Our second step now is we need to interpret our value for R2 as the proportion of variants explained. So that means we need to take our 0.3481, which is written as a decimal currently, and we need to turn it into a percentage, so we need to multiply by 100. And when we do, we will find that it's equal to 34.81% or approximately equal to 35%. Or we could simply round our decimal point as well to. Once again, we can take our R squared value, and it will be simply equal to 0.35 when we round to two decimal places to match all of our multiple choice answers. So that is it. We've officially solved for this particular problem. So, once again, our final and third step, let's make our final conclusions, so we can state that 35% of the variation in product sales is explained by advertising expenditure. So that means our current. The answer without a doubt will have to be multiple choice answer letter A, which once again is 0.35% and 35% of the variation in product sales is explained by advertising expenditure. And that's it. That's 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.

"Old Vehicles In Exercises 31–34, use the figure shown at the left.33. Coefficient of Determination Find the coefficient of determination r^2 and interpret the results."

Watch next

"Old Vehicles In Exercises 31–34, use the figure shown at the left.

33. Coefficient of Determination Find the coefficient of determination r^2 and interpret the results."