Linear regression algorithm

To truly understand linear regression, it is helpful to know how the algorithm works. The code for ols() is hundreds of lines because it has to work with any formula and any dataset. However, in the case of simple linear regression for a single dataset, you can implement a linear regression algorithm in just a few lines of code.

The workflow is:

First, write a function to calculate the sum of squares using this general syntax:

def function_name(args):
  # some calculations with the args
  return outcome

Second, use scipy's minimize function find the coefficients that minimize this function.

The explanatory values (the n_convenience column of taiwan_real_estate) are available as x_actual. The response values (the price_twd_msq column of taiwan_real_estate) are available as y_actual.

minimize() is also loaded.

This exercise is part of the course

Intermediate Regression with statsmodels in Python

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Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Complete the function
def calc_sum_of_squares(coeffs):
    # Unpack coeffs
    ____, ____ = ____
    # Calculate predicted y-values
    y_pred = ____ + ____ * ____
    # Calculate differences between y_pred and y_actual
    y_diff = ____ - ____
    # Calculate sum of squares
    sum_sq = ____
    # Return sum of squares
    return sum_sq
  
# Test the function with intercept 10 and slope 1
print(calc_sum_of_squares([10, 1]))

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