EMET2007 Lecture 4

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Unformatted text preview: ics and simple linear regression) EMET2007/6007 13 th March 2013 36 / 50 Again with p values H0 : β 1 = 0 H 1 : β 1 6 = 0 We are just interested in whether there is an e¤ect and have to expectation that it will be positive or negative p value = 0.000 and tb = 4.08 > 0 β 1 Pr (jt678 j > 1.645) = 0.05 and Pr (jt678 j > 2.33) = 0.01 The null hypothesis is rejected since 0.000 < 0.05 Conclude that there is evidence that family income has an e¤ect on expected birth weight of children Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 37 / 50 Testing more general hypotheses about a regression coe¢ cient Null hypothesis H0 : β 1 = a t-statistic tb = β 1 b β a estimate hypothesised value =1 standard error β se b1 The test works exactly as before, except that the hypothesized value is subtracted from the estimate when forming the statistic Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 38 / 50 Example: Campus crime and enrollment An interesting hypothesis is whether crime increases by one percent if enrollment is increased by one percent c log (crime ) = 6.63 + 1.27 log (enroll ) (1.03 ) 2 (0.11 ) n = 97 R = 0.585 b is di¤erent from one, but is this di¤erence statistically signi…cant? β1 H0 tb β 1 β 1 = 1 H1 : β 1 6 = 1 1.27 1 = = 2.45 > 1.96 0.11 : The hypothesis is rejected at the 5% level Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 39 / 50 Con…dence intervals b βi βi s tn 2 βi s tn 2 se b βi s βi + tn se bi β b βi L ecture 4 (econometrics and simple linear regression) EMET2007/6007 b βi 2 se b βi 13 th March 2013 40 / 50 Con…dence intervals 0 Pr Pr b1 β tn tn Pr ( tn Pr @ tn 2 ,0 .025 se 2 ,0 .025 se b βi b β1 Lecture 4 (econometrics and simple linear regression) Pr (jtn 2 ,0 .025 2 ,0 .025 b βi β1 b βi tn βi se bi β 2j 2 = 0.95 tn 2,0.025 ) = 0.95 1 2 ,0 .025 ) tn tn 2 ,0 .025 A = 0.95 b β1 = 0.95 tn 2 ,0 .025 se b + tn β1 2 ,0 .025 se βi EMET2007/6007 b βi = 0.95 13 th March 2013 41 / 50 Con…dence intervals Often we are not interested in just the speci…c value of an estimate,...
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This note was uploaded on 06/15/2013 for the course EMET 2007 taught by Professor Strachan during the Two '13 term at Australian National University.

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