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  3. Statistical Thinking in Python (Part 2)
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Exercise

How is it optimal?

The function np.polyfit() that you used to get your regression parameters finds the optimal slope and intercept. It is optimizing the sum of the squares of the residuals, also known as RSS (for residual sum of squares). In this exercise, you will plot the function that is being optimized, the RSS, versus the slope parameter a. To do this, fix the intercept to be what you found in the optimization. Then, plot the RSS vs. the slope. Where is it minimal?

Instructions

100 XP
  • Specify which values of the slope for which to compute the RSS. Use np.linspace() to get 200 points in the range between 0 and 0.1.
  • Initialize an array, rss, to contain the RSS using np.empty_like().
  • Write a for loop to compute the sum of RSS of the slope. Hint: the RSS is given by np.sum((y_data - a * x_data - b)**2). The variable b you computed in the last exercise is already in your namespace.
  • Plot the RSS versus slope. Be sure to label your axes.
  • Show your plot.