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Exercise

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.

Instructions 1/2

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Complete the function body.

  • Unpack coeffs to intercept and slope, respectively.
  • Calculate the predicted y-values as the intercept plus the slope times the actual x-values.
  • Calculate the differences between actual and predicted y-values.
  • Calculate the sum of squares: square the differences in y-values and take the sum.
  • Return the sum of squares.