Question

A regression analysis is conducted with 9 observations.

a. What is the df value for inference about the slope β​?

b. Which two t test statistic values would give a​ P-value of 0.01 for testing H0​: β=0 against Ha​: β ≠​0?

c. Which​ t-score would you multiply the standard error by in order to find the margin of error for a

99% confidence interval for β​?

Answer 1

A regression analysis is conducted with 9 observations.

n=9

a) degree of freedom value for inference about the slope β is

df=n-2

df=9-2=7

Regression analysis is conducted with 9 observations. The degrees of freedom are 7.

b)

For testing H0​: β=0 against Ha​: β ≠​0, the test statistic equals:

Where b is the sample slope and se denotes its standard error

Using t critical table for a two-tailed test with alpha = 0.01 and df (7), we get

t- critical = -3.499425 and 3.499425  

Therefore, t test statistic = -3.499425, 3.499425

c)

(c) From part (b), we have calculated t critical value = 3.499

So, we will multiply the standard error by 3.499 to get the margin of error

t critical = 3.499