Topic 4- Linear
Regression Model with One
Regressor
Consider population interest
a of
-
Take an i id sample from this population
-
. :
(Y 1 ,
X 1) , (42 ,
X2) , . . . . (Yn .
Xn)
Linear
regression model
-
:
Yi = Bo + B + Xi + Hi For i =
1 , .... n
Random variable ; represents all of the characteristics
Parameters OF unit i that are unobserved by the researcher
(coefficients)
Yi =
dependent variable
Xi independent variable ;
regressor; covariate
=
Hi =
error term ; omitted variable
Func toon -
Population regression line :
X Bo + B= X
Intercept Slope
Exogeneity (mean independence) assumption :
E(Ui(xi) =
0 For i =
1 , .... n
Implication of exogeneity assumption :
E(Yi (xi) =
ElBo + Baxi + ni(Xi) O
=
ElBo(Xi) + ElBIXi(Xi) + Elui(Xi)
=
Bo + B+ X ;
Cov(Ui , Xi) = Corr (Ui ,
xi) =
0
,
,
Regression Model with One
Regressor
Consider population interest
a of
-
Take an i id sample from this population
-
. :
(Y 1 ,
X 1) , (42 ,
X2) , . . . . (Yn .
Xn)
Linear
regression model
-
:
Yi = Bo + B + Xi + Hi For i =
1 , .... n
Random variable ; represents all of the characteristics
Parameters OF unit i that are unobserved by the researcher
(coefficients)
Yi =
dependent variable
Xi independent variable ;
regressor; covariate
=
Hi =
error term ; omitted variable
Func toon -
Population regression line :
X Bo + B= X
Intercept Slope
Exogeneity (mean independence) assumption :
E(Ui(xi) =
0 For i =
1 , .... n
Implication of exogeneity assumption :
E(Yi (xi) =
ElBo + Baxi + ni(Xi) O
=
ElBo(Xi) + ElBIXi(Xi) + Elui(Xi)
=
Bo + B+ X ;
Cov(Ui , Xi) = Corr (Ui ,
xi) =
0
,
,
