I have a question on interpreting whether our residual plot meets this assumption. In class, we were told if there was a pattern, the homosce. assumption has been violated. However, from other readings, it seems that if the points create a rectangular "scatter", it has met this assumption. I'm confused. Could you please give some further details about how to interpret this plot appropriately!
Thanks!
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The stuff that you have read is correct. I guess it is confusing that how come a rectangular shape, which has a pattern, does not violate the assumption but meets the assumption.
Homoscedasticity is tested by a scatter plot of residuals. Residuals are errors, ie. actual score in population - predicted score. The line in the middle of the scatter plot is the mean of Y, ie. the mean of predicted scores.
If you get a rectangular shape of residuals around the line, that means that the residuals are evenly distributed around the mean. This is a good thing. Because homoscedasticity means equal variance of residuals, ie. the variance between the mean of y (the line, or y=0, which means no error) and the errors is homogeneous. So, getting a rectangular shape, which your graph may look like this...
o o o o o
o o o o o o
o o o o o
________________________________ y
o o o o o o o o
o o o o o o
o o o o o o
(note: dots are residuals)
You can see that the residuals that is furthest away from the line above and below, from left to right have almost equal distance from the line. This is homoscedasticity.
In contrast, if you get a pattern, such as a "blow horn", which look like this...
o o o
o o o o o
o o o o o o o
o o o o o o o
o o o o o o
________________________________ y
o o o o o o o o
o o o o o o
o o o o o o
o o o o
o o o o
o o
You can see how the residuals actually fan out. That is a bad sign! The residuals that are the variance on the left hand side of the graph is small while the variance on the right hand side is huge. The variance of the residuals across the graphs are not homogeneous! So, the blow horn shape definitely violates the assumption of homoscedasticity, because this is heteoskedasticity.
Also, just a reminder, there is rule of tumb for you the check this assumption as well. The assumption is violated when the highest variance is 10 times bigger than the lowest variance, ie. with a ratio of 10:1.
Hope this helps. I'm really having fun with plotting graph with letters. :P
I'm not satisfied with the graphs... I'll make a new post by putting actual graphs.
Thanks Grace!
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