Let's say we have some data :
- input data X with shape (1, N=100), this will be duplicated 1000 times.
- target data Y with shape (S=1000, N=100).
We have 1000 experimental data points, samples.
My question is, will it make a difference if we do Polynomial Regression on all target data, or if we first take a mean of data Y and then we try to do the regression?
If we use all data, then we can reshape it to be : X=(1000*100, 1) Y=(1000*100, 1)
If we use mean data : X=(100, 1) Y=(100, 1)
My guess is that it might look similar, but when we apply cross validation and try to find the most optimal degree or bandwidth, the error will be connected to the variance of the data. But it is just my assumption, I could not find an answer online, so I appreciate any help, thank you.