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# Regression Model, Omitted Bias and F-Stat

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The following regression model represents the demand for peanut butter:

log qt = B1 + B2 logpt + B3log rt + B4logmt + ut

where qt is the quantity of peanut butter consumed at time t; pt is the
price of peanut butter; rt is the price of jelly; and mt is income per
capita. Suppose an analyst estimates the following model:
log qt = B1 + B2 logpt + B3logmt + et
we expect B2 < 0 (law of demand) and B4 > 0 (peanut butter is a
normal good). What is the sign of omitted variable bias of B2 if

(a) B3 < 0 (peanut butter and jelly are complements) and pt and rt
are positively correlated.
(b) B3 > 0 (peanut butter and jelly are substitutes) and pt and rt are
positively correlated.
(c) B3 < 0 (peanut butter and jelly are complements) and pt and rt
are negatively correlated.

2. Test the null hypothesis that all coefficients except the intercept
equal to 0.

lwage = 1 + 2educ + 3married + 4exper + 5exper2 + et

storage display value
variable name type format label variable label
-------------------------------------------------------------------------------
lwage float %9.0g log(wage)
id int %9.0g person identifier
exper byte %9.0g age - educ - 6
expersq int %9.0g exper^2
married byte %9.0g =1 if married, 1976
IQ int %9.0g IQ score
KWW byte %9.0g knowledge world of work score
motheduc byte %9.0g mother's schooling
fatheduc byte %9.0g father's schooling
educ byte %9.0g years of schooling, 1976
nearc4 byte %9.0g =1 if near 4 yr college, 1966
nearc2 byte %9.0g =1 if near 2 yr college, 1966
weight float %9.0g NLS sampling weight, 1976

Source | SS df MS Number of obs = 3003
-------------+------------------------------ F( 4, 2998) = 212.57
Model | 130.571897 4 32.6429744 Prob > F =
Residual | 460.389254 2998 .153565462 R-squared =
Total | 590.961151 3002 .196855813 Root MSE = .39187

------------------------------------------------------------------------------
lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ | .0898329 .0035461 25.33 0.000 .0828799 .0967859
married | -.0350949 .0035839 -9.79 0.000 -.042122 -.0280678
exper | .077507 .0070715 10.96 0.000 .0636416 .0913724
expersq | -.0021298 .0003347 -6.36 0.000 -.0027861 -.0014735
_cons | 4.667204 .0706975 66.02 0.000 4.528584 4.805825