Lecture 34- Hypothesis Test for the Slope Parameter

Question 1

What does it mean if the slope or beta 1 is 0?

Answer 1

There is no linear relationship between the two variables (horizontal line).

Question 2

What are we testing in the hypothesis test for the slope parameter?

Answer 2

Testing if the slope is actually 0, in other words we assume that there is no relationship

Question 3

What form will our test statistic take for the slope?

Answer 3

t= (estimate- null) / standard error

t= (estimate of beta 1- 0)/ standard error of beta 1

Question 4

If the null hypothesis is correct what distribution will the sampling distribution for the slope take?

Answer 4

A t distribution with n-2 degrees of freedom

Question 5

How come the t distribution follows a degrees of freedom of n-2

Answer 5

Degrees of freedom is how much the data can vary. The -2 comes from the fact that we are estimating 2 parameters.

Question 6

Complete the analysis in r for the example on slides 652 to 656

Answer 6

answers in slides

Question 7

Complete a hypothesis test by hand for the data on slide 654

Answer 7

Work though/ answers on slide 659 and 660

Question 8

What does a p value of less than 0.05 show in a hypothesis test for the slope parameter?

Answer 8

Shows the test statistic is extreme and unlikely to come from the null distribution (where slope is 0). Likely therefore that that alternative hypothesis is true and the slope is not 0, there is a linear relationship between the two variables.