Question

A regression analysis is conducted with 13 observations.

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

b. Which two t test statistic values would give a​ P-value of

0.05 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

95%confidence interval for betaβ​?

Answer 1

Answer:

Given that:

A regression analysis is conducted with 13 observations

a) What is the df value for inference about the slope betaβ​?

A regression analysis is conducted with 13 observations The degrees of freedom are df =n-2 Since, here n= 13

The degrees of freedom are df = n-2

df =13-2

df = 11

A regression analysis is conducted with 13  observations. The degrees of freedom are 11

b) Which two t test statistic values would give a​ P-value of 0.05 for testing H0​:β =0 against Ha​: β ≠​0?

For testing    against   the test statistic equals

Where b Is the sample slope and se denotes its standard  error. Based on the t-score test statistic and the degrees of freedom, we determine the P-value From the t-Distribution Calculator, two t test statistic values with = n-2= 13 -2=11 would give a P-value of 0.05 for testing

  and are

Therefore, the f test statistic values are and  

c) Which​ t-score would you multiply the standard error by in order to find the margin of error for a 95%confidence interval for beta β​?

From the t Distribution Calculator, the t-score with  df = n-2 = 13-2 =11 is 2.2009.

A 95% confidence interval for has formula

Where, me= margin of error, we would multiply the standard error by 2.2009 in order to find the margin of error for a 95% confidence interval for .