Lecture 40- Multiple Linear Regression 2

Question 1

What is this lecture largely about?

Answer 1

Accessing whether our model for multiple linear regression is any good

Question 2

What does adding in parameters do?

Answer 2

Adding in variables change estimates for parameters, change the model

Question 3

Do the hypothesis test on slide 766…

Answer 3

Answers on slide

Question 4

Read the R output on slide 767 and determine which variables in the multiple linear regression are valuable and what needs to got rid of

Answer 4

Answers in slide/ notes

Question 5

What T distribution does multiple linear regression follow when trying to complete a hypothesis test?

Answer 5

n-k-1

Question 6

Is it fine to leave in variables that aren’t significant to the model?

Answer 6

No, they can be detremetrial as create extra noise

Question 7

When you refit a variable what do you have to make sure you do?

Answer 7

You need to refit the model to find the optimal parameter estimates

Question 8

Read output on slide 776 and calculate a 95% confidence interval…

Answer 8

Answers on slide

Question 9

What assumptions does multiple linear regression need to follow?

Answer 9

Linearity: There is a straight line relationship between µY and xj
when all other predictor variables are held constant.

Independence The responses Y1, Y2, . . . , Yn are statistically
independent.

Normality The error terms e1, e2, . . . , en come from a normal
distribution.

Equal variance The errors terms all have the same variance, σ
2 ‘homoscedastic’)

Plotting residuals against fitted values is useful for this