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TASMANIAN SCHOOL OFBUSINESS AND ECONOMICSBEA 674 Data and BusinessDecision MakingWeek 12 Multiple Linear Regression AnalysisDr Jing Tian, UTAS1
ObjectivesIn this week, we will learn:•How to use a multiple linear regression modelto explain the variation of a dependentvariable.•How to interpret the OLS estimated interceptand slopes.•How to compare models with different numberof independent variables.•How to test and construct CI estimate forindividual marginal effect.•How to test for joint significance.2
Hypothesis TestingFor Joint Significance•We would like to test hypothesis which involvesmore than oneβ–e.g. We want to test whether price of pies andspending on advertisements collectively help toexplain pie sales.•This sort of test that involves more than oneparameter is called joint hypothesis test.𝐻0: ?1= ?2= 0𝐻𝐴: at least one of the above parameters is not zero (not H0)3012iiiiQPA=+++
•To perform joint hypothesis tests we compare:–the SSE from a regression which assumesthat H0is true (this is the restricted SSE orSSER) with–SSEU, which is the SSE from the original(unrestricted) regression.•In the pie example, the original/unrestrictedmodel is.•The restricted model is when H0is trueHypothesis TestingFor Joint Significance012iiiiQPA=+++**0iiQ=+4
•F-test statistic:•Under H0 ,•A small value of F will be consistent with H0,while large value of F will support HAHypothesis TestingFor Joint Significance()()(1)m is the number of restrictionsn-(k+1) is the d.o.f. of the unrestricted modelRUUSSESSEmFSSEnkwhere−=−+,(1)~m nkFF−+5
•Example:If F follows F2,12,then P(F>3.885)=0.05F Distribution0= .053.885Reject H0Do notreject H0F2,12d.o.f. for thenumeratord.o.f. for thedenominator6
Critical Values of the F DistributionUpper Tail Area12345678910111213141516