Linear regression with defined intercept

Question

I have a DataFrame (df) with two columns and three rows.

Column X = [137,270,344] Column Y = [51, 121, 136]

I want to get the slope of the linear regression considering the intercept = 0.

I have tried to add a point (0,0) but it doesn´t work.

EX. Column X = [0, 137,270,344] Column Y = [0, 51, 121, 136]

The code that I am using.

Code:

X= df [“Column X”].astype(float)  
Y = df [“Column Y”].astype(float)  

slope, intercept, r_value, p_value, std_err = stats.linregress(X, Y)
intercept_desv = slope 
coef_desv = intercept  

I expected intercept = 0 but is less than 0.

Answer 1

In standard linear regression, all data points implicitly have a weight of 1.0. In any software that allows linear regression using weights, the regression can effectively be made to pass through any single point - such as the origin - by assigning that data point an extremely large weight. Numpy's polyfit() allows weights. Here is a graphing example with your data using this technique to make the fitted line pass through the 0,0 point.

import numpy, matplotlib
import matplotlib.pyplot as plt

xData = numpy.array( [0.0, 137.0, 270.0, 344.0])
yData = numpy.array([0.0, 51.0, 121.0, 136.0])

weights = numpy.array([1.0E10, 1.0, 1.0, 1.0]) # heavily weight the 0,0 point
#weights = None # use this for "no weights"

polynomialOrder = 1 # example straight line

# curve fit the test data
fittedParameters = numpy.polyfit(xData, yData, polynomialOrder, w=weights)
print('Fitted Parameters:', fittedParameters)

modelPredictions = numpy.polyval(fittedParameters, xData)
absError = modelPredictions - yData

SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
print()
print('Predicted value at x=0:', modelPredictions[0])
print()


##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    # first the raw data as a scatter plot
    axes.plot(xData, yData,  'D')

    # create data for the fitted equation plot
    xModel = numpy.linspace(min(xData), max(xData))
    yModel = numpy.polyval(fittedParameters, xModel)

    # now the model as a line plot
    axes.plot(xModel, yModel)

    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot

graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)