# implementing an algorithm that mixes data clustering and linear regression

i have the following dataframe available in the link as a csv, it conveys information about stars.

more specifically - column ID represents arbitrary ID of sample. column z represents my target variable (response). the other columns represent the attributes available for each sample (predictors) and their corresponding measurement errors.

i used the following code to reduce the 11D data to 3 principal components and plotted the scatter of the data in principal space (with color indicating of the target variable Z)

from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler

#first we remove the target z and ID from the dataset and standredize it (mean=0 and std=1)
pca = PCA(n_components=3)
data_for_pca=data_clean.iloc[:,2:13]
data_for_pca=StandardScaler().fit_transform(data_for_pca)
#now we perform the pca and get the amount of variance, or relative information that each new component holds.
principal_c=pca.fit_transform(data_for_pca)
pd.DataFrame(pca.explained_variance_ratio_).transpose()

import matplotlib.cm as cmx
from mpl_toolkits.mplot3d import Axes3D
def scatter3d(x,y,z, cs, colorsMap='jet'):
cm = plt.get_cmap(colorsMap)
cNorm = matplotlib.colors.Normalize(vmin=min(cs), vmax=max(cs))
scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=cm)
fig6 = plt.figure()
ax6 = Axes3D(fig6)
ax6.scatter(x, y, z, c=scalarMap.to_rgba(cs))
ax6.set_xlabel('pc1',fontweight='bold')
ax6.set_ylabel('pc2',fontweight='bold')
ax6.set_zlabel('pc3',fontweight='bold')

scalarMap.set_array(cs)
fig6.colorbar(scalarMap)

plt.show()
scatter3d(principal_c[:,0],principal_c[:,1], principal_c[:,2],np.array(data.iloc[:,1]))


i attached the dataframe and code so anyone can reproduce and observe the 3d plot from all directions, my main intention with this question is to check if my intuitive analysis of the results is good and how to implement my idea on predicting z from the predictor data.

i see that the dots have somewhat of a smooth spherical gradient centered - roughly speaking - at (-2.5,-1,-0.25). perhaps i should implement some kind of gaussian kernel? if that's a good idea, how can i implement it?

another observation is that the data is slightly clustered in "plates" (as can be seen .

maybe i should perform seperate linear regression for each cluster/plate. and let the algorithm classify each point to a cluster/plate, then for each cluster/plate i can infer the target with the more sensitive linear regression coefficients.

if you think that might work, how should i implement it?

maybe there's a more rigorous approach to the further analysis of the PCA? (i mean that i'm kinda using my eyes to decide what is best to do but i'm sure there's a computational approach to the task).

would love to hear opinion and advice, this is a solo project that is part of an attempt to get a better understanding of data science after a BSc in physics.