The coefficient of determination r^2 is the ratio of which two...

Question

The coefficient of determination r^2 is the ratio of which two types of variations? What does r^2 measure? What does 1 - r^2 measure?

Accepted Answer

Below there. Today we're going to 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 a regression model yields a coefficient of determination R2 is equal to 0.82. What does this value indicate about the model and what does 1 minus R2d represent? Awesome. So it appears for this particular problem we're asked to solve for two separate answers. Our first answer is we're asked to determine what R2 equals 0.82. What does that value indicate about this particular regression model? That's our first answer, and our second answer is we're asked, what does 1 minus R squared represent? So with that in mind, let's read off our multiple choice answers to see what our final answer pair might be now that we know what we're trying to solve for. So A is 82% of the variation is explained by the model, 18% is unexplained, B is 18% of the variation is explained by the model, 82% is unexplained. C is 81% of the variation is unexplained and 18% is explained, and D is 100% of the variation is explained by the model, 0% is unexplained. Awesome. So, our first step that we need to take in order to solve this particular problem is we need to recall a note that R2 equals 0.82 means that 82% of the total variation in the dependent variable is explained by the regression model. So I'll put a giant E to represent explained. So let's say that again. So ultimately what we need to be able to recognize and recall is that for this particular problem, R2 equals 0.82 means that 82% of the total variation in the dependent variable is explained by the regression model. So, with that in mind, our second step now is we need to note and recall that 1 minus R squared is equal to 1 minus 0.82, which is equal to 0.18. So that means That when we convert 0.18 to a percentage, that will mean that 18% of the variation is not explained by the model. So I'll call it NE not explained. Fantastic. So once again, 1 minus R squared is equal to 0.18, which is 18%, so 18% of the variation is not explained by the model. So that will mean our third and final step. We can therefore state that 82% of the variation is explained. And 18% of the variation, so once again, 18% is unexplained, which I'll call UE for short, so unexplained. So once again, 82% is explained and 18% is unexplained, and this corresponds with multiple choice answer letter A, which once again states that 82% of the variation is explained by the model. And 18% is unexplained. And that's it. Those are our final answers. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

The coefficient of determination r^2 is the ratio of which two types of variations? What does r^2 measure? What does 1 - r^2 measure?

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