Great video but at t=517 , you said if the curve bends then it is not linear, it is actually not linear in X , but still linear for the parameters B that you are concerned with so it's still a linear model!
Hi, I have a question about the nature of the residuals. I have been thinking about the nature of the residuals with respect to the value of the response variables (y). Is there any benefit of normalizing each residual value to the fitted value of the model? For example, if raw residual data suggested a constant spread (homoscedastic) across y (or x) one might think this is okay, as the model consistently does not provide more or less accuracy depending on the position (x,y) within the model. But, say this residual was +/- 1 unit at the low y values, and likewise +/- 1 unit at larger y values (as I said, "constant"). However, if my understanding is correct, this 'error' is not constant in terms relative to the value of the response (y) variable. At low response values this +/- 1 residual value may be something like 50% of the actual y value, but at higher y values this same raw residual value may only be a fraction of the response value. Even though the raw residuals are constant, the relative residuals (as a fraction of the response variable that they encompass) may be severely heteroscedastic. Is this sort of normalization to the residuals commonly done or of benefit? Or make any sense? Thanks for your videos by the way, these are wonderfully effective.
In general, statistics doesn't care about the raw metric of the variable. You can analyze Y or a scaled Y and the metrics are the same (except for the ones that are scale-dependent, such as the slope and intercept). Because of this, stats models don't care about relative residuals (because the scale of the variables are arbitrary). They only care about raw residuals (or sometimes scaled residuals). Does that answer your question?
The only statistical videos that feel like watching a movie-informative, engaging, and a total treat to watch!
This video is EXCELLENT. Especially the visuals. Thanks!
Ah shucks. Thanks :)
this video feels like a saturday morning cartoon except now I learned something for my statistics 2 course
I think I would be frightened if you spoke to me like this in person
This was a very informative vid. 15:39 very well spent.
Great video but at t=517 , you said if the curve bends then it is not linear, it is actually not linear in X , but still linear for the parameters B that you are concerned with so it's still a linear model!
It is! I'm actually making a video right now about polynomial regression :)
Hi, I have a question about the nature of the residuals. I have been thinking about the nature of the residuals with respect to the value of the response variables (y). Is there any benefit of normalizing each residual value to the fitted value of the model? For example, if raw residual data suggested a constant spread (homoscedastic) across y (or x) one might think this is okay, as the model consistently does not provide more or less accuracy depending on the position (x,y) within the model. But, say this residual was +/- 1 unit at the low y values, and likewise +/- 1 unit at larger y values (as I said, "constant"). However, if my understanding is correct, this 'error' is not constant in terms relative to the value of the response (y) variable. At low response values this +/- 1 residual value may be something like 50% of the actual y value, but at higher y values this same raw residual value may only be a fraction of the response value. Even though the raw residuals are constant, the relative residuals (as a fraction of the response variable that they encompass) may be severely heteroscedastic. Is this sort of normalization to the residuals commonly done or of benefit? Or make any sense? Thanks for your videos by the way, these are wonderfully effective.
In general, statistics doesn't care about the raw metric of the variable. You can analyze Y or a scaled Y and the metrics are the same (except for the ones that are scale-dependent, such as the slope and intercept). Because of this, stats models don't care about relative residuals (because the scale of the variables are arbitrary). They only care about raw residuals (or sometimes scaled residuals). Does that answer your question?
Content is great, but the background music is annoying.