Office Hours this week:

• Wednesday 10a
• Wednesday 2p
• Thursday 10a

You want to predict mpg using weight and automatic. Write out how you would calculate $\hat{\beta }$ in matrix form using the data provided (you need not solve the matrices)

Solving the equation results in the following $\hat{\beta }$:

$\left[\begin{array}{c}{\hat{\beta }}_0\\ {\hat{\beta }}_1\\ {\hat{\beta }}_2\end{array}\right]=\left[\begin{array}{c}80.45\\ -18.40\\ -13.30\end{array}\right]$

Using the information provided, calculate the MSE (mean squared error) for this model.

$\left[\begin{array}{ccccc}0.66& 0.34& 0.07& 0.19& -0.26\\ 0.34& 0.66& -0.07& -0.19& 0.26\\ 0.07& -0.07& 0.37& 0.42& 0.21\\ 0.19& -0.19& 0.42& 0.55& 0.02\\ -0.26& 0.26& 0.21& 0.02& 0.77\end{array}\right]$

Above is the hat matrix for the model. Use this to calculate LOOCV error for this model

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

Using the data above, calculate ${\pi }_k$, ${\mu }_k$, and ${\sigma }^2$

Using LDA, what is are the discrimant scores for x = 3? Which class would you classify this point into?

What is the probability that an observation where x = 3 is in class 1?

What is the decision boundary for this LDA problem?

P(+ | Drug User) = 0.8

P(Drug User) = 0.1

P(+ | Not a drug user) = 0.2

• What is the probability of being a drug user give you test positive?

• What is the accuracy?
• What is the false positive rate?
• What is the false negative rate?