"Graphical Analysis In Exercises 1–3, use the figure.

Question

1. Describe the total variation about a regression line in words and in symbols."

Accepted Answer

Hello everybody and welcome back. Our next problem says. In a study examining the relationship between study hours and test scores, a linear regression line was fitted to the data. One student studied for 6 hours and scored 82 while the average test score of all students was 75. Which of the following best describes the total variation for the student? A, the squared distance between the student's predicted score and their actual score. So, the difference Yi minus Y hat I squared. the square distance between the predicted score and the mean score. So the difference y hat I minus y bar, that's squared. See the square distance between the actual score and the mean score. The difference yi minus y bar, that difference squared. And finally the difference between the student score and the regression slope. So, first of all, we're talking about variation. So, that's gonna involve squaring the difference. So, we can eliminate choice D, which just has a difference. So it should be squared. No matter what the difference is. So recall that the variation we're talking about a sample like this, is made up of the explained. And unexplained. Variation. So, the total, which encompasses both of these, is going to be choice C, the square difference between the actual score and the mean score. So explain the entire difference between the actual score that we've seen, presented to us, and then the mean or total average, in this case that's 75. Look at our remaining answer choices, when we talk about square distance with the students predicted score and their actual score, that's going to be the unexplained. Variances. Which makes logical sense if you think of it, because the various factors that we're aware of go into predicting a score. So then we say, well, why isn't our actual score the same as the predicted one, predicted based on the regression line, that would be an unexplained difference. But not the total variation. Then choice B is squared distance between predicted score and mean score. This is the explained. Variation. So again, that makes sense. We had a predicted score and then the difference between the predicted and the mean score. is based on other factors we might not be able to have full knowledge of. So choice B isn't correct. So it's more, we're talking about total variation for a particular student when average test score is 75. And which of our statements best describes total variation, and that is C, the squared distance between the actual score and the mean score. See you in the next video.

"Graphical Analysis In Exercises 1–3, use the figure.1. Describe the total variation about a regression line in words and in symbols."

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"Graphical Analysis In Exercises 1–3, use the figure.

1. Describe the total variation about a regression line in words and in symbols."