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  3. Statistical Thinking in Python (Part 2)

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 versus the slope. Where is it minimal?

Instructions

100 XP
  • Specify the values of the slope to compute the RSS. Use np.linspace() to get 200 points in the range between 0 and 0.1. For example, to get 100 points in the range between 0 and 0.5, you could use np.linspace() like so: np.linspace(0, 0.5, 100).
  • Initialize an array, rss, to contain the RSS using np.empty_like() and the array you created above. The empty_like() function returns a new array with the same shape and type as a given array (in this case, a_vals).
  • 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. Here, fertility is the y_data and illiteracy the x_data.
  • Plot the RSS (rss) versus slope (a_vals).
  • Hit submit to see the plot!