print surface fit equation in python

Question 1

I'm trying to fit a surface model to a 3D data-set (x,y,z) using matplotlib.
Wherez = f(x,y).
So, I'm going for the quadratic fitting with equation:

f(x,y) = ax^2+by^2+cxy+dx+ey+f

So far, I have successfully plotted the 3d-fitted-surface using least-square method using:

# best-fit quadratic curve       A = np.c_[np.ones(data.shape[0]), data[:,:2], np.prod(data[:,:2], axis=1), data[:,:2]**2]       C,_,_,_ = scipy.linalg.lstsq(A, data[:,2])       #evaluating on grid         Z = np.dot(np.c_[np.ones(XX.shape), XX, YY, XX*YY, XX**2, YY**2], C).reshape(X.shape)

But, how can I be able to print/get the fitted equation of the surface(with coefficient values) ?

I little help will be highly appreciated.
thank you.

Question 2

Can you post the code corresponding to "So far, I have successfully plotted the 3d-fitted-surface using least-square method"?

Question 3

@etna added the fitting section used as per your comment.

Question 4

Ok... according to the documentation of the function scipy.linalg.lstsqdocs.scipy.org/doc/scipy-0.15.1/reference/generated/… the estimated coefficients should be stored in your variableC soprint C seems a reasonable thing to do :)

Question 5

@etna wow! that did the work... But can I print the equation on canvas with the corresponding coefficients ?

Question 6

The same as in A so here constant first etc. A way to print your equation is this:print 'f(x,y) = {:.2f}x^2+{:.2f}y^2+{:.2f}xy+{:.2f}x+{:.2f}y+{:.2f}'.format(C[4],C[5],C[3],C[1],C[2],C[0]) (But make sure I ordered the coeffs right). Another way:print 'f(x,y) = {4:.2f}x^2+{5:.2f}y^2+{3:.2f}xy+{1:.2f}x+{2:.2f}y+{0:.2f}'.format(*C).

Question 7

According to the documentation of the function scipy.linalg.lstsqhttp://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.linalg.lstsq.html the estimated coefficients should be stored in your variable C (the order corresponding to columns in A).

To print your equation with estimated coefficients showing 2 digits after decimal point:

print 'f(x,y) = {:.2f}x^2+{:.2f}y^2+{:.2f}xy+{:.2f}x+{:.2f}y+{:.2f}'.format(C[4],C[5],C[3],C[1],‌C[2],C[0])

or:

print 'f(x,y) = {4:.2f}x^2+{5:.2f}y^2+{3:.2f}xy+{1:.2f}x+{2:.2f}y+{0:.2f}'.format(*C)

By the way, librariespandas andstatsmodels can be very helpful for this kind of task (e.g. checkRun an OLS regression with Pandas Data Frame )

Question 8

thanks for the suggestion regarding panda. But can I also check the goodness of fit(or p-value) using the current code. ?

Question 9

To the best of my knowledge, there is no "shortcut" so you need to compute the coefficients' standard errors (e.g.thetarzan.wordpress.com/2012/10/27/…), then compute the t statistic and finally get your p value...

Question 10

Do this least square fitting function provide us some R value ? I'm not being able to locate it.

etna 1,0837 silver badges13 bronze badges · Accepted Answer · 2017-05-23 11:58:35Z

According to the documentation of the function scipy.linalg.lstsqhttp://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.linalg.lstsq.html the estimated coefficients should be stored in your variable C (the order corresponding to columns in A).

To print your equation with estimated coefficients showing 2 digits after decimal point:

print 'f(x,y) = {:.2f}x^2+{:.2f}y^2+{:.2f}xy+{:.2f}x+{:.2f}y+{:.2f}'.format(C[4],C[5],C[3],C[1],‌C[2],C[0])

or:

print 'f(x,y) = {4:.2f}x^2+{5:.2f}y^2+{3:.2f}xy+{1:.2f}x+{2:.2f}y+{0:.2f}'.format(*C)

By the way, librariespandas andstatsmodels can be very helpful for this kind of task (e.g. checkRun an OLS regression with Pandas Data Frame )

thanks for the suggestion regarding panda. But can I also check the goodness of fit(or p-value) using the current code. ?
To the best of my knowledge, there is no "shortcut" so you need to compute the coefficients' standard errors (e.g.thetarzan.wordpress.com/2012/10/27/…), then compute the t statistic and finally get your p value...
Do this least square fitting function provide us some R value ? I'm not being able to locate it.

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print surface fit equation in python

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