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true, it is rejected in, for example, 5% of the cases.
In the following example, this is the point of the tdistribution with
1386 degrees of freedom that is exceeded in 5% of the cases. ! Reject if t statistic less than Lecture 4 (econometrics and simple linear regression) 1.645 EMET2007/6007 13 th March 2013 31 / 50 L ecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 32 / 50 “Statistically signi…cant” variables in a regression
If a regression coe¢ cient is di¤erent from zero in a twosided test, the
corresponding variable is said to be “statistically signi…cant”
If the number of degrees of freedom is large enough so that the
normal approximation applies, the following rules of thumb apply: Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 33 / 50 Guidelines for discussing economic and statistical signi…cance
If a variable is statistically signi…cant, discuss the magnitude of the
coe¢ cient to get an idea of its economic or practical importance
The fact that a coe¢ cient is statistically signi…cant does not
necessarily mean it is economically or practically signi…cant!
If a variable is statistically and economically important but has the
“wrong” sign, the regression model might be misspeci…ed
If a variable is statistically insigni…cant at the usual levels (10%, 5%,
1%), one may think of dropping it from the regression
If the sample size is small, e¤ects might be imprecisely estimated so
that the case for dropping insigni…cant variables is less strong Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 34 / 50 In this example we wish to know if a family’ income in 1988 (in $1,000s)
s
(faminc ) explains baby’ birth weight (in ounces) (bwght ) :
s
bwghti
bwghti = β0 + β1 faminci + εi
= b0 + b1 faminci + bi
β
β
ε
= 115.27 + 0.118faminci + bi
ε The Stata output with n = 1388, has R 2 = 0.0119 and Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 35 / 50 H0 : β 1 = 0 H 1 : β 1 6 = 0
One would either expect a positive e¤ect of class attendance on GPA
tb =
β
1 b
β1 se b1
β df = 1388 = 0.118
= 4.08
0.029
2 = 1386 Pr (jt678 j > 1.645) = 0.05 and Pr (jt678 j > 2.33) = 0.01 The null hypothesis is rejected since tb
β 1 = 4.08 > 1.645 Conclude that there is evidence that family income has an e¤ect on
expected birth weight of children Lecture 4 (econometr...
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 Two '13
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