LO 3.2.2.C

Learning Objective: Calculate the F-statistic given TSS, RSS, n, and p.

Review:

The hypothesis test for multilinear regression is performed by computing the F-statistics

$<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mfenced><mrow><mi>T</mi><mi>S</mi><mi>S</mi><mo>-</mo><mi>R</mi><mi>S</mi><mi>S</mi></mrow></mfenced><mrow><mi>R</mi><mi>S</mi><mi>S</mi></mrow></mfrac><mo>·</mo><mfrac><mfenced><mrow><mi>n</mi><mo>-</mo><mi>p</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mi>p</mi></mfrac></math>$

TSS is the total sum of squares

RSS is the residual sum of squares

p is the number of predictors

n is the number of instances in the dataset

When there is no relationship between the response and predictors, one would expect the F-statistic to take on a value close to 1. On the other hand, if the alternative hypothesis Ha is true we expect F-statistic to be greater than 1.