Lecture 38- Hypothesis test for Logistic Regression

Question 1

Draw what a positive logistic curve would look like and then a negative logistic curve….

Answer 1

Answers on slide on slide 728

Question 2

What is the null and alternative hypothesis for logistic regression? What acts as evidence against the null?

Answer 2

• Null: beta 1= 0
• Alternative: beta 1 doesn’t equal 0
• Essential when slope is 0 there is no relationship (the explanatory variable x is not predicting y)
• The further away our test statistic is from 0 the greater the evidence is against the null, there is a relationship

Question 3

What function do you put in r to obtain the p value?

Answer 3

2*pnorm(abs(z), lower.tail= FALSE)

Question 4

What does abs mean?

Answer 4

Absolute

Question 5

How do we calculate the z (test statistic)?

Answer 5

Estimated parameter for slope/ standard error for slope (beta 1)

Question 6

For logistic regression does x have to be continuous?

Answer 6

No, it is common to use it for contingency tables where both x and y are binary variables with 2 outcomes

Question 7

Complete the example on slide 735 to do a hypothesis test for contingency table/ binary logistic regression…

Answer 7

Answers in slides

Question 8

What is the basic idea of logistic regression? What is a hypothesis test useful for?

Answer 8

• Logistic regression is the modification of linear regression for binary response variables
• We model how the log odds of a y=1 response changes with a predictor variable x
• Testing via hypothesis test for the slope parameter can be used to access evidence that the probability of y=1 depends on x