Data Analysis week 7

Question 1

What is the residual e_i defined as

Answer 1

The difference between the datapoint y_i and the predicted value. So y_i = alpha * x_i + beta + e_i

Question 2

What is the residual sum of squares

Answer 2

The residual sum of squares (RSS) is e_1^2 + e_2^2 + … + e_n^2. It measures how badly the model explains the data (in its loss function).

Question 3

What is the relation between alpha and beta and the RSS

Answer 3

Computing alpha and beta with the covariance results in the regression model with the smallest possible RSS.

Question 4

What is a loss function

Answer 4

Functions that show how badly a model explains data.

Question 5

What is another example of a loss function

Answer 5

The mean absolute error

Question 6

What is so special about RSS as a loss function

Answer 6

The values for alpha and beta that minimize RSS can be mathematically derived, while for other loss functions, you need a computer for this. And RSS can be motivated by viewing linear regression as a statistic model.

Question 7

What other role can the normal distribution play

Answer 7

The normal distribution can be an approximation of the residuals.

Question 8

What do likelihood functions tell you

Answer 8

Likelihood functions tell you how good your model is. Likelihood is high when your model is good.