we need to add a dummy variable ‘ones’ whose value is always 1 to X so we use np.hstack() method but if i use the method as X = np.hstack((ones, X)) then after prediction i am getting a linear prediction curve for all value of tau…but if I use X = np.hstack((X, ones )) then the prediction curve is changing accordingly as change in tau …Why?
Delimma in using np.hstack() method
hey @maitraanirban25 ,
you know that a general linear equation is like y = a0*1 + a1x1 + a2x2 + a3x3 +…
where x1,x2,x3… are our features of data , a1,a2,a3… are there respective coefficients and a0 is the intercept.
so to get that intercept term we use np.hstack((ones,X))
to explain this , lets assume a from X as [ 2,5,6,8 ]
so after np.hstack((ones,X)) we get X=[ 1,2,5,6,8] agree?
lets say we have our coefficient as C = [ 0.2, 0.1, 0.3, 0.2,0.4 ]
So now if we calculate our y as by multiplying each feature with respective coefficient and then summing them up
we get y = 0.2 + 0.2 +1.5 +1.2+3.2 = 6.3
but if we would have taken np.hstack((X,ones)) and keeping the coefficients as same
we would be getting
X = [ 2,5,6,8 ,1] and C = [ 0.2, 0.1, 0.3, 0.2,0.4 ]
y = 0.4 + 0.5 + 1.8 + 1.6 + 0.4 = 4.7
So as you see, the algorithm has a defined manner to calculate it , which your intercept to be at first , so when you change the position of intercept value , coefficients of all other feature changes , along with intercept one. Hence , when you plot it , it result in a linear curve depending upon the tau value.
I hope this would have helped you to understand the reason behind it.
Thank You and Happy Learning 
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Thanks Bhaiya … nice explanation
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