Chapter 3 Exercise Hints

8. Auto, simple regression

8.a. smf.ols is how to do a regression

8.a.i relationship means the coefficient

8.a.iv this would be get_prediction and its summary_frame

8b. sns.lmplot is the way to get the points and a regression line

8c. Diagnostic plots means the plot_lm_summary function that i wrote. Follow the instructions on wy-cs.site.

9. Auto, multivariate regression

  • Scatterplot matrix is sns.pairplot
  • Pandas has a corr() function that works on data frames
  • Again, this is smf.ols … you specify all of the variables you want to consider by listing them in the formula “x1+x2+stuff”. Statistically significant response means looking at results.pvalues.
  • plot_lm_summary again. The “*” creates a new variable by multiplying. The “:” also includes the individual terms automatically. You can include “log(x1)” in your formula. You may need to do np.power(horsepower,2) if you want to consider what happens when a single predictor is squared. See the StatsModels formula page for more information.

10. Carseats, categorical variables

10f. Comparing fit with different models could be done with the material from page 79ff.

10g. Outliers and high leverage points are visible on the summary plots.

11. t-statistic

Opening paragraph:

  • In order to set a random seed, you use numpy.random.seed(N).
  • The normal distribution is scipy.stats.norm().
  • Sampling 50 values from any distribution is whatever.rvs(size=50)
  • Standard deviation is set by the scale= parameter to the normal distribution.

11a. To perform a regression without an intercept, use the formula the text suggests: “y ~ x + 0”. You can get $t$-values and $p$-values from the instance variables tvalues and pvalues if you want to see them individually.

13. Simulated data

See number 11 for the functions needed.

  • 13a. See Exercise 11 for how to sample from the normal distribution.

  • 13f. The population regression line could be drawn by creating a data frame with only two points in it (both lying on the desired line). Use sns.lineplot in the same cell as the scatterplot to draw the line. Skip the legend if it does not appear automatically. Example code

    trueLine = pd.DataFrame({'x': np.array([-3,   3]), 
                         'y': np.array([-10, 10])})

14. Collinearity with simulated data

See question 11 for a primer on simulated data.

14g. To add the bad data based on the original dataframe df:

badData = pd.DataFrame({'x1': 0.1, 'x2': 0.8, 'y': 6}, 
                       index=[len(df)])
df2 = df.append(badData)

This question needs to be unpacked. Use the plot_lm_summary function that was provided in class to analyze leverage.