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Interpreting Computer Output For Regression Article Khan Academy

Leo Migdal
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interpreting computer output for regression article khan academy

In other videos we've done linear regressions by hand, but we mentioned that most regressions are actually done using some type of computer or calculator. So, what we're going to do in this video is look at an example of the output that we might see from a computer, and to not be intimidated by it. We’ll also see how it gives us the equation for the regression line and some of the other data it gives us. Here, it tells us Cheryl Dixon is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake in milligrams and the number of hours spent studying. A scatter plot of the data showed a linear relationship.

This is a computer output from a least squares regression analysis on the data. We have these things called the predictors, coefficient, and then we have these other things: standard error of coefficient, t, and p. Then all of these things down here, how do we make sense of this in order to come up with an equation for our linear regression? Let's just get straight on our variables. Let's just say that we say that y is the thing that we're trying to predict. So, this is the hours spent studying, hours studying.

Then, let's say x is what we think explains the hours studying. Here's one of the things that explains the hours studying, and this is the amount of caffeine ingested. So, this is caffeine consumed in milligrams. Our regression line would have the form y hat. This tells us this is a linear regression that is trying to estimate the actual y values for given x's is going to be equal to mx plus b. Now, how do we figure out what m and b are based on this computer output?

In this section we’ll be going over the different parts of the linear model output. First, we’ll talk about the coefficient table, then we’ll talk about goodness-of-fit statistics. Let’s re-run the same model from before: First, summary() helpfully reiterates the formula that you put in. This is useful to check that it’s running what you thought it ran. It also tells you the minimum, 1st quantile (25%-ile), median, 3rd quantile (75%-ile), and maximum of the residuals (\(e_i = Y_i - \hat{Y_i}\)).

That is, the minimum residual error of this model is -1.0781, the median residual error is 0.1260, and the maximum is 1.5452. Let’s turn next to the coefficient table. This video explains how to interpret the output from a computer-generated linear regression analysis and how to use it to determine the equation for the regression line. The video discusses how to interpret a computer-generated output from a linear regression analysis. It focuses on understanding the variables, coefficients, and other information provided by the output. The main goal is to determine the equation for the regression line that can be used for prediction.

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