Scikit linear model predictions not matching

Question

I'm using scikits linear model for modelling two input variables and one output variable. I suspect that the two input variables have a quadratic relationship with the output variable. So I created the data set ($a^2$, $b^2$, $ab$, $a$, $b$, $1$) for the two original input variables $a$ and $b$, then used the scikits linear model for this data which gave the coefficients:

[ 0.21746023  0.3457555  -0.15043191 -0.15318758 -0.27072946  0.        ]

the .predict() method produces very good predictions however, when I run the code

for i in data:
    print i[0]*coeffs[0]+i[1]*coeffs[1]+i[2]*coeffs[2]+i[3]*coeffs[3]+i[4]*coeffs[4]+i[5]*coeffs[5]

The outputs do not match the predictions at all. Here is my full code:

def import_data():
    data=np.genfromtxt("input_file")
    y=data[:,2]
    all_data=[(a**2,b**2,a*b,a,b,1) for (a,b,c) in data]
    return np.array(all_data),y

def main():
    data,y=import_data()

    regr = linear_model.LinearRegression()
    regr.fit(data, y)
    coeffs=regr.coef_
    print coeffs
    for i in data:
        print i[0]*coeffs[0]+i[1]*coeffs[1]+i[2]*coeffs[2]+i[3]*coeffs[3]+i[4]*coeffs[4]+i[5]*coeffs[5]
    print regr.score(data, y)
    print regr.predict(data)

Could someone tell me where my code is wrong?

Answer 1

I found the error, so I guess I'll answer my own question. Apparently the intercept term is not part of the coefficient vector, its a separate thing, so that has to be added onto the linear combination. So here is the correct code

for i in data:
        print i[0]*coeffs[0]+i[1]*coeffs[1]+i[2]*coeffs[2]+i[3]*coeffs[3]+i[4]*coeffs[4]+regr.intercept_