Question

A regression analysis is conducted with 15 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 0.01for testing H0​: β=0 against Ha​: β≠​0? (Use a comma to seperate answers)

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​? (Round to three dec. places)

Answer 1

a) For testing for the slope coefficient, the degrees of freedom is given as:
Df = n - 2 = 13
Therefore 13 is the degrees of freedom here.

b) As this is a two tailed test, we have from t distribution tables:
P( t₁₃ < 3.012) = 0.995

Therefore, due to symmetry, we get here:
P( -3.012 < t₁₃ < 3.012) = 0.99

Therefore -3.012, 3.012 are critical values here.

c) We would use the same critical value for slope coefficient as in the above part which is given as 3.012. Therefore 3.012 is the required t-score here.