Question

Residual sum of squares - regression

Hello

So the residual sum of squares tells us how well our model fit. I know it's supposed to be close to zero to be a good fit, but when is it a bad fit?

I have the values:

11.6

37.11

1.8

3.5

Of course the two last are good values, but what about 37.11 and 11.6? Would I still say that the model is farily good?

Answer 1

If you are comparing the Residual sum of squares of these 4 from the same type of data, then 37.11 is not good followed by 11.6. As you mentioned of, course, the closer to zero is better.

As such, it all depend on what is your measured value. If for example you measures a very minute quantity as for example weight of impurities in a compound(it will be very minute (microgram)compaed to sample weight(gm). When teh sample weight is in teh order of 200 gms, and the impurity weight 0.0000023 gm and in the second case the residual SS will be much less when comared to sample weight. So enough care should be taken as whether we are comparing teh same quantity at different times then an absolute comarison is advised. When we compare the residual SS of different quantities or unrelated things like GPA and height, then definitely we can not compare them as an egg-egg tpe of things.