Lecture 37- Logistic Regression

Question 1

When do we use logistic regression?

Answer 1

• To model data that has a binary outcome

- Can be used to examine the effect of x on the probability of a given outcome

Question 2

In logistic regression if the probability of y=1 is p what is the probability of y=0?

Answer 2

1-p

-The are complimentary events either the outcome of the binary event is a success or it isn’t

Question 3

What shape is a logistic curve?

Answer 3

S shaped

P greater than O goes positive way (hill last)
P less than 0 goes negative way (hill first)

Question 4

What is the logistic model given by?

Answer 4

logit (p)= log (p/ (1-p))= b naught + b 1 times x

Question 5

In the logistic regression model what is p/ (p-1)? What happens when you logs this?

Answer 5

The odds of the event y=1 occurring, so when log this it is the log odds

Question 6

What is beta naught and beta 1 in a logistic regression model?

Answer 6

• Beta naught is the log odds when x=0, i.e. the y intercept

- Beta 1 is the gradient i.e. the change in the log odds for a unit increase in the predictor variable x

Question 7

What is maximum likelihood estimation used for?

Answer 7

To estimate regression coefficients

Question 8

Interpret the table on slide 721? What value would you pull out as important?

Answer 8

Answers on slide

Question 9

What does increase x by one unit result in? Use this info to go from the log odds to the odds for the newt and shade example on slide 724?

Answer 9

A multiplicative change of e^b1 to the odds

Answers on slides