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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 lm() 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

  1. Write a script to calculate the sum of squares.
  2. Turn this into a function.
  3. Use R's general purpose optimization function find the coefficients that minimize this.

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.

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  • Set the intercept to ten.
  • Set the slope to one.
  • 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. Get the sum of the differences in y-values, squaring each value.