Python Multiple Linear Regression using OLS code with specific data?

Question

I am using the ols.py code downloaded at scipy Cookbook (the download is in the first paragraph with the bold OLS) but I need to understand rather than using ra

Answer 1

You should differentiate two cases: i) you just want to solve the equation. ii) you also want to know the statistical information about your model. You can do i) with np.linalg.lstsq; and for ii), you better use statsmodels.

Below you find a sample example, with both solutions:

# The standard imports
import numpy as np
import pandas as pd

# For the statistic
from statsmodels.formula.api import ols

def generatedata():
    ''' Generate and show the data '''
    x = np.linspace(-5,5,101)
    (X,Y) = np.meshgrid(x,x)

    # To get reproducable values, I provide a seed value
    np.random.seed(987654321)   

    Z = -5 + 3*X-0.5*Y+np.random.randn(np.shape(X)[0], np.shape(X)[1])

    return (X.flatten(),Y.flatten(),Z.flatten())

def regressionmodel(X,Y,Z):
    '''Multilinear regression model, calculating fit, P-values, confidence intervals etc.'''

    # Convert the data into a Pandas DataFrame
    df = pd.DataFrame({'x':X, 'y':Y, 'z':Z})

    # Fit the model
    model = ols("z ~ x + y", df).fit()

    # Print the summary
    print(model.summary())

    return model._results.params  # should be array([-4.99754526,  3.00250049, -0.50514907])

def linearmodel(X,Y,Z):
    '''Just fit the plane'''

    M = np.vstack((np.ones(len(X)), X, Y)).T
    bestfit = np.linalg.lstsq(M,Z)[0]
    print('Best fit plane:', bestfit)

    return bestfit

if __name__ == '__main__':
    (X,Y,Z) = generatedata()    
    regressionmodel(X,Y,Z)    
    linearmodel(X,Y,Z)