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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
tstatistic
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.
 Two '13
 strachan

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