# Review

Lucy D’Agostino McGowan

# Make sure to bring a calculator to the exam

## Exam

• Two parts
• Part 1: In class Monday (you can have one cheat sheet)
• Part 2: The same exam, taken at home – this is open notes (there will be no class Wednesday so you can have dedicated time to work on this then)
y x1 x2
5.7 2 1
8.3 3 1
7.3 4 0

You want to predict y using x1 and x2 write out how you would calculate $\hat\beta$ in matrix form using the data provided (you do not need to solve the matrix)

y x1 x2
5.1 2 1
6.9 3 1
7.8 4 0

Solving the above equation results in the following:

$\begin{bmatrix} \hat\beta_0 \\\hat\beta_1\\\hat\beta_2 \end{bmatrix} = \begin{bmatrix} 0.7\\1.8\\0.9 \end{bmatrix}$

Using the information provided, calculate the MSE for this model.

y x1 x2
9.1 4 1
6.2 3 0
5.8 2 1

You get a new test data set (above). Using the model you fit to the training data, calculate the MSE in this test set.

## Logistic Regression

term estimate std.error statistic p.value conf.low conf.high
(Intercept) 12.04 4.51 2.67 0.01 5.21 23.63
wt -4.02 1.44 -2.80 0.01 -7.70 -1.83

We are predicting whether a car has automatic transmission based on it’s weight

How do you interpret $\hat\beta_1$ is this a marginal or conditional effect?

## Logistic Regression

term estimate std.error statistic p.value conf.low conf.high
(Intercept) 25.89 12.19 2.12 0.03 5.60 55.83
wt -6.42 2.55 -2.52 0.01 -12.82 -2.37
mpg -0.32 0.24 -1.35 0.18 -0.87 0.12

How do you interpret $\hat\beta_1$? Is this a conditional effect?

## Penalized Regression

• What is the penalty for Ridge Regression?
• What is the penalty for Lasso?
• What is the equation for Elastic Net?
• How do we choose $\lambda$? $\alpha$?

• As $\lambda$ increases in penalyzed regression, how does this impact the flexibility of the model?
• What are the advantages/disadvantages of a small $k$ vs large $k$