Question

A simple linear least squares regression of the heights (in feet) of a building on the number of stories in the building was performed using a random sample of 30 buildings. The associated ANOVA F statistic was 5.60. What is the P-value associated with this ANOVA F test?

a.) greater than 0.10

b.) between 0.001 and 0.01

c.) between 0.01 and 0.025

d.) between 0.05 and 0.10

e.) between 0.025 and 0.05

f.) less than 0.001

Answer 1

Solution:

Given: A simple linear least squares regression of the heights (in feet) of a building on the number of stories in the building was performed using a random sample of 30 buildings.

thus k = number of independent variables = 1 and n = sample size = 30

thus

df_regression = k = 1

df_error = n- k - 1= 30 - 1 - 1 = 28

The associated ANOVA F statistic was 5.60.

F_STAT = 5.60

We have to find P-value associated with this ANOVA F test.

Look in F table, for df_regression = df_numerator = 1 and df_error = df_denominator = 28

and find interval in which F = 5.60 fall. Then find corresponding right tail area interval , which is P-value interval.

F = 5.60 fall between 4.20 and 5.61 and corresponding right tail area in ascending order is between 0.025 and 0.050

Thus correct option for P-value is:

e.) between 0.025 and 0.05