"Some type of non-linear curve "might better fit the data," or the relationshipīetween the y and the x is non-linear. X-axis and then above, then it might say, "Hey, a linear model "might not be appropriate. This, where on the residual plot you're going below the I'm going down here, but then I'm going back up. When I look at just the residual plot, it doesn't look like But if we see something like this, a different picture emerges. And so I would say thatĪ linear model here, and in particular, this regression line, is a good model for this data. But like the example we just looked at, it looks like these residualsĪre pretty evenly scattered above and below the line. The actual is slightly above the line, and you see it right over And once again, you see here, the residual is slightly positive. So right here you have a regression line and its corresponding residual plot. Of other residual plots? And let's try to analyze them a bit. To do a non-linear model." What are some examples This line isn't a good fit, "and maybe we would have Up and then curving down, or they had a downward trend, then you might say, "Hey, Upward trend like this or if they were curving But if you do see some type of trend, if the residuals had an Or randomly scattered above and below this line, you don't really discern any trend here, then a line is probably a The general idea is if you see the point pretty evenly scattered Of how good a fit it is and whether a line is good at explaining the relationship between the variables. Whether the regression line is upward sloping or downward sloping, this gives you a sense Now, one question is why do people even go through the trouble of creating a residual plot like this. I have just created, where we're just seeing, for each x where we haveĪ corresponding point, we plot the point above or below the line based on the residual. And then this last point, the residual is positive. Residual is negative one, so we would plot it right over here. So for one of them, the residual is zero. When we have the point two comma three, the residual there is zero. When x equals two, weĪctually have two data points. So this right over here, weĬan plot right over here. One, expected was 0.5, one minus 0.5 is 0.5. What was the residual? Well, the actual was So those are the residuals,īut how do we plot it? Well, we would set up or axes. So six minus 5.5, that is a positive 0.5. When x equals three is six, our expected when x equals three is 5.5. The expected, two timesĢ.5 minus two is three, so this is going to be two minus three, which equals a residual of negative one. So our residual over here, once again, the actual is y equals two when x equals two. For this point right over here, the actual, when xĮquals two, for y is two, but the expected is three. 5, so we have a positive, we have a positive 0.5 residual. This point right over here? For this point here, the actual y when x equals one is one, but the expected, when x equals one for this least squares regression line, 2.5 times one minus two, well, that's gonna be. So how do I make that tangible? Well, what's the residual for So what is a residual? Well, just as a reminder, your residual for a given point is equal to the actual minus the expected. What I'm going to do now is plot the residualsįor each of these points. We actually came up with the equation of this So right over here, we have a fairly simple Going to do in this video is talk about the idea of a residual plot for a given regression and the data that it's trying to explain.
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