Econometrics Quiz 2 Term
Solutions(100% A+)
Regression Analysis - ANS-a study of relationship between one variable with one or
more variables
Dependent and Independent Variables - ANS-the independent variables are used to
explain the dependent variable
Explained and Explanatory Variables - ANS-the explanatory variables are used to
explain the explained variables
Population Regression and Sample Regression - ANS-PRF: represents the regression
line in the population as a whole
E(Y|Xi)=B1 + B2X2 (nonstochastic PRF)
Yi=B1 + B2Xi + ui (stochastic)
SRF: use a sample and its results to estimate B1 with b1 and B2 with b2
Yhat= b1 + b2X (Predicted Value)
Y= b1 + b2X + e (Actual Value)
Two Variable and Multiple linear Regression - ANS-Two Variable- the dependent
variable is a function of just one explanatory variable
Multiple- a regression in which more than one independent variable is used to explain
the behavior of the dependent variable
Method of Ordinary Least Squares - ANS-a method of estimating parameters for a
regression analysis in such a way of finding b1 and b2 by minimizing ��e^2
Parameter Estimates and their Meaning - ANS-b1 is the intercept and this doesn't have
much economic value
b2 etc. are slopes; consider Δx by one unit
Linear in Variables and Linear in Parameters - ANS-linear in variables means that the
, X's are raised to the first power
linear in parameters means that b1 etc are raised to the first power (<- this is the one
that is required for Linear Regression)
Total Sum of Squares - ANS-the total variation of the actual Y values about their sample
mean Ybar, squared
��(Y-Ybar)^2 or ��y^2 TSS
Explained (Regression) Sum of Squares - ANS-variation in Y explained by X(=Yhat)
around its mean value
��(Yhat-Ybar)^2 or ��yhat^2ESS
Unexplained (Residual) Sum of Squares - ANS-unexplained variation of the Y values
about the regression line
��e^2 RSS
Normal equations - ANS-b1=Ybar - b2 Xbar
b2=(��xy)/(��x^2)
Assumptions of CLRM
-Linear in Parameters- - ANS-the dependent variable is a linear function of the
parameters, B's, it may or may not be linear in the variables
Assumptions of CLRM
-u uncorrelated to X- - ANS-the explanatory variables are uncorrelated with the
disturbance term u
Assumptions of CLRM
-zero mean of u- - ANS-given the value of X, the expected, or mean, value of the
disturbance term u is 0
Assumptions of CLRM
-homoscedastic variance of u- - ANS-the variance of each u is constant
(cf heteroscedasticity)
Assumptions of CLRM
-no autocorrelation- - ANS-no correlation between two error terms
Cov(ui,uj)=0 ⩝ ui≠uj
Solutions(100% A+)
Regression Analysis - ANS-a study of relationship between one variable with one or
more variables
Dependent and Independent Variables - ANS-the independent variables are used to
explain the dependent variable
Explained and Explanatory Variables - ANS-the explanatory variables are used to
explain the explained variables
Population Regression and Sample Regression - ANS-PRF: represents the regression
line in the population as a whole
E(Y|Xi)=B1 + B2X2 (nonstochastic PRF)
Yi=B1 + B2Xi + ui (stochastic)
SRF: use a sample and its results to estimate B1 with b1 and B2 with b2
Yhat= b1 + b2X (Predicted Value)
Y= b1 + b2X + e (Actual Value)
Two Variable and Multiple linear Regression - ANS-Two Variable- the dependent
variable is a function of just one explanatory variable
Multiple- a regression in which more than one independent variable is used to explain
the behavior of the dependent variable
Method of Ordinary Least Squares - ANS-a method of estimating parameters for a
regression analysis in such a way of finding b1 and b2 by minimizing ��e^2
Parameter Estimates and their Meaning - ANS-b1 is the intercept and this doesn't have
much economic value
b2 etc. are slopes; consider Δx by one unit
Linear in Variables and Linear in Parameters - ANS-linear in variables means that the
, X's are raised to the first power
linear in parameters means that b1 etc are raised to the first power (<- this is the one
that is required for Linear Regression)
Total Sum of Squares - ANS-the total variation of the actual Y values about their sample
mean Ybar, squared
��(Y-Ybar)^2 or ��y^2 TSS
Explained (Regression) Sum of Squares - ANS-variation in Y explained by X(=Yhat)
around its mean value
��(Yhat-Ybar)^2 or ��yhat^2ESS
Unexplained (Residual) Sum of Squares - ANS-unexplained variation of the Y values
about the regression line
��e^2 RSS
Normal equations - ANS-b1=Ybar - b2 Xbar
b2=(��xy)/(��x^2)
Assumptions of CLRM
-Linear in Parameters- - ANS-the dependent variable is a linear function of the
parameters, B's, it may or may not be linear in the variables
Assumptions of CLRM
-u uncorrelated to X- - ANS-the explanatory variables are uncorrelated with the
disturbance term u
Assumptions of CLRM
-zero mean of u- - ANS-given the value of X, the expected, or mean, value of the
disturbance term u is 0
Assumptions of CLRM
-homoscedastic variance of u- - ANS-the variance of each u is constant
(cf heteroscedasticity)
Assumptions of CLRM
-no autocorrelation- - ANS-no correlation between two error terms
Cov(ui,uj)=0 ⩝ ui≠uj
