1. What is a residual? Explain when a residual is positive, ne...

Question

1. What is a residual? Explain when a residual is positive, negative, and zero.

Accepted Answer

Hello 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. If the observed value for a data point is 12 and the predicted value from the regression model is 9, what is the value of the residual and is it positive, negative, or zero? Awesome. So it appears for this particular problem we're trying to determine what is the value of the residual, and once we determine the value of the residual, we're asked to determine whether or not it's positive, negative, or zero. So now that we know we're ultimately trying to solve for, let's read off our multiple choice answers to see what our final answer pair might be, noting once again we're trying to solve for two separate answers. We're trying to figure out the value for the residual, and then we're determining for our second answer if it's positive, negative, or zero. So A is 3 and positive, B is -3 and negative. C is 21 and and D is 0 and 0. Awesome. So our first step is we need to determine what the residual is, and we need to recall a note that the residual is calculated as Y minus Y hat. So with that in mind, our second step now is we need to substitute in our known variables and solve for the residual. So let us know that the problem itself tells us that Y is equal to 12 and Y hat is equal to 9, so we need to take 12 minus 9, which is simply equal to 3, and this is a positive 3. So that is our first answer that we're trying to solve for. So now, let us quickly note that since 3 is greater than 0, that will mean that the residual is positive and that is our second answer. So therefore, without a doubt, the answer is 3 positive because 3 is greater than 0. So that means looking at our multiple choice answers. The correct answer has to be letter A, which once again is 3 and positive. And that's it. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

1. What is a residual? Explain when a residual is positive, negative, and zero.

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