Perform the Global Test for Utility FTest Explain your concl

Perform the Global Test for Utility (F-Test). Explain your conclusion.

DeVry Math 533

Solution

• Rather than testing B(beta) each individually, we use a global test that
encompasses all B’s and test the following overall hypothesis:\\

H0 : B1 = B2 = ... = Bk = 0
Ha : at least one Bj is not equal to 0.

• The test statistic to test this hypothesis is called Fstatistic and is
calculated as:
F = ((SSyy SSE)/k)/MSE = (R^2/k)/(1 R^2)/[n (k + 1)

• The F statistic is the ratio of

– the explained variability (as reflected by R^2) and
– the unexplained variability (as reflected by 1 R^2),

each divided by the corresponding degrees of freedom.

• The larger the F statistic, the more useful the model.

• Critical value for the test: F ,numdf,denomdf (three subscripts: a(alpha),
numerator degrees of freedom and denominator degrees of freedom).
• We use F-table
• Each table corresponds to a different a: 0.1, 0.05, 0.025 and 0.01.
• We search the table using the numerator degrees of freedom (column)
and the denominator degrees of freedom (rows):
Numerator d.f. = k
Denominator d.f. = n (k + 1)

• For example, if a = 0.1, n = 20 and k = 4, F(0.1,4,15) = 2.36
• The F statistic for the model is given by both SAS and JMP directly
on the output. SAS calls it ”‘F Value”’ and JMP calls it ”‘F Ratio”’.
• Both SAS and JMP compute the F-statistic as:
F = Model Mean Square
Error Mean Square
and the degrees of freedom are:
Numerator df = Model df = k
Denominator df = Error df = n (k + 1).