Testing A Subset Of Regression Coefficients 12.5

Front 1

In the last section, we presented an F test for testing all the coefficients in a regression model and a t test for testing ________ coefficient. Another F test of the null hypothesis tests that several of the true __________ are _______—that is, that several of the predictors have no value given the others.

Back 1

one, coefficients, zero

Front 2

The idea is to compare the SS(Regression) or R^2 values when certain variables given other variables are excluded and when they are included in the prediction equation. When they are included, the R2 is automatically at least as _________ as the R2 when they are excluded because we can predict at least as well with more __________ as with less. Similarly, SS(Regression) will be larger for the complete model.

Back 2

large, information

Front 3

The F test for this null hypothesis tests whether the gain is more than could be expected by ___________ alone.

Back 3

chance

Front 4

k= the total number of predictors
g= the number of predictors with coefficients not hypothesized to be zero (g < k),

Then k - g represents the number of predictors with coefficients that are hypothesized to be ______. The idea is to find SS(Regression) values using all predictors (the complete model)

and using only the g predictors that do not appear in the null hypothesis (the reduced model).

Back 4

zero

Front 5

F Test of a Subset of Predictors

H0:bg+1=bg+2 =...=bk=

Back 5

Memorize