STAT451 HW1: Practice with Python, hard-margin SVM, and linear regression solution

1. Use a hard-margin SVM

to classify cars as having automatic or manual transmissions.

• Read https://www.stat.wisc.edu/~jgillett/451/01/mtcars30.csv into a DataFrame. (This is the mtcars data frame from R with two of its rows removed to get linearly separable data.)
• Make a 30×2 numpy array X from the mpg (miles per gallon) and wt (weight in 1000s of pounds) columns. Make an array y from the am column (where 0=automatic or 1=manual transmission).
• Train an SVM using kernel=’linear’ and C=1000. Print its coefficients and intercept.
• Report the training accuracy. (It’s given by clf.score(X, y).)
• Predict the transmission for a car weighing 4000 pounds (wt=4) that gets 20 mpg.
• Use five plt.plot() calls to make a figure with wt on its x-axis and mpg on its y-axis including:
  • the automatic transmission cars in red
  • the manual transmission cars in blue
  • the decision boundary (the center line of the road)
  • the lower margin boundary (the left side of the road)
  • the upper margin boundary (the right side of the road)
  • a reasonable title, axis labels, and legend

2. Make three linear regression models.

2a: Make a simple regression model by hand.

Use the matrix formula $w=(X^{T}X{)}^{-1}{X}^{T}y$ we developed in class to fit these three points: (0, 5), (2, 1), (4, 3). (Use linear_model.linearRegression(), if you wish, to check your work.)

… your answer here (just give the model, $y=wx+b$) …

2b: Make a simple linear regression model from real data.

Estimate the average daily trading volume of a Dow Jones Industrial Average stock from its market capitalization. That is, use $y=$ AvgVol vs. $x=$ MarketCap.

• Read https://www.stat.wisc.edu/~jgillett/451/data/DJIA.csv into a DataFrame.
• Find the model. Print its equation.
• Print its $R^2$ value (the proportion of variability in $y$ accounted for by $x$ via the linear model, given by model.score(X, y)).
• Use the model to predict the volume for a company with market capitalization of 0.25e12 (a quarter-trillion dollars); add this as a red point on your plot.
• Say what happens to Volume as Market Capitalization increases. (Use a Markdown cell.)

2c. Make a multiple regression model.

Estimate the same volume from both market capitalization and price. That is, use $y=$ AvgVol vs. $x_1=$ MarketCap and $x_2=$ Price.

• Find the model.
• Print its equation.
• Print its $R^2$ value.
• Say what happens to Volume as Market Capitalization increases and what happens to Volume as Price increases. (Use a Markdown cell.)