3/18 FINISH

for multiple regression models, what can you test?

whether subsets of coefficients are equal to 0.

why would you compare 2 regression models (full & reduced)?

to determine whether it’s worthwhile to include the the additional variables

full model

all k explanatory variables are included

reduced model

the variables x_l+1, …, x_k have been removed (the variables you’re questioning the importance of)

can a reduced model include any explanatory variables that aren’t in the full model?

no

what does the partial F-test do?

compare 2 regression models

example question (partial F-test)

is the full model significantly better than the reduced model at explaining the variation in y?

for the partial F-test, what do the hypotheses represent?

H_o = reduced model

H_a = full model

ex. of hypotheses for partial F-test

H₀ : β₁ = β₄ = β₅ (variables you’re testing importance of)

H_a : at least of the coefficients isn’t equal to 0.

ex. of hypotheses interpretation for a partial F-test

H₀: Match rate, age, and total number of employees at the firm together do NOT explain a significant amount of variation in participation rate when the total number of 401k participants and the total number of eligible employees are already in the model.

H_a: At least one of the variables, match rate, age, and/or total number of employees at the firm, explains a significant amount of variation in participation rate when the total number of 401k participants and the total number of eligible employees are already in the model.

if H₀ is not rejected, what model should you choose?

reduced

if H₀ is rejected, which model should you choose?

full model

F test statistic formula FOR PARTIAL F TEST / HYPOTHESES

(SSE_R - SSE_F)/(k-l) / SSE_F/(n-k-1)

F

full model

R

reduced model

k

number of x variables in full model

l

number of x variables in reduced model

what variables should you add when building the reduced model in Excel?

the variables that AREN’T the ones you’re testing the importance of

formula for obtaining the p-value for F-test in Excel

F.DIST.RT

ex. of interpretation when failing to reject partial F-test

market share and competitor’s sales were simultaneously tested for inclusion in the model and were found to be non-significant at the alpha = 0.05 level when advertising and bonuses were already in the model, F_{(2, 20)} = 0.303, p = .7419. (use full model)