Econometrics - Regression analysis || with Complete Solutions.
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Course
Econometrics - Regression analysis
Institution
Econometrics - Regression Analysis
Regression analysis correct answers measures the impact of a set of variables on another variable.
Largely concerned with ESTIMATING/predicting the population mean or average value of the dependent variable based on the known values of the explanatory variable
There are two Variables X and Y,...
Econometrics - Regression analysis || with Complete
Solutions.
Regression analysis correct answers measures the impact of a set of variables on another
variable.
Largely concerned with ESTIMATING/predicting the population mean or average value of the
dependent variable based on the known values of the explanatory variable
There are two Variables X and Y, representing the same population. How does changing X effect
Y
e.g E(Y | Xi) = f (Xi)
Regression analysis (simple) correct answers concerned with the study of the relation between
the dependent and explanatory variable(s).
the estimated mean value of x based on the value of y
denoting the dependent variable correct answers Y
the explained/response/ endogenous variable
denoting the explanatory variable correct answers X
the independent/regressive/ exogenous variable
direction of travel correct answers changes in X having an impact on Y (important with
regression)
The Population regression function (PRF) / Conditional expectation function (CEF) correct
answers E(Y | Xi) = f (Xi)
The expected or average value of one random variable, called the dependent or explained
variable, as a function the values of one or more other variables, called the independent or
explanatory variables.
E(Y given X), conditional expectation function (CEF) correct answers this is the point on the
regression line
the average value of the dependent variable Y given the value of exogenous variable X
Simple linear regression model correct answers an equation that describes the straight-line
relationship between a dependent variable and an independent variable
, y = B0 + B1Xi + u
where B0 is the intercept, u is the error and B1x is the regression line
population regression line correct answers the mean value of the dependent variable
corresponding to each value of the X variable. The line passing through the conditional means of
Y.
Joining the conditional mean values of Y for each X value.
E(Y | Xi) = f (Xi) = B1 + B2Xi
where B1 is the intercept coefficient, and B2 is the slope coefficient. Both unknown but fixed
parameters.
stochastic specification of the population regression function correct answers Yi = B1 + B2Xi +
ui
where B1 + B2Xi is the systematic/modeled/deterministic component and u is the
stochastic/random error term the non systematic/random component
u is a random variable
correct answers there is a distribution of points around every exogenous variables conditional
mean, this distribution is u.
The difference between actual data point and the conditional mean is u.
correct answers u is a random variable of which the regession line is the mean for each variable,
as it doens't depend on X. This is why stats has to do so many corrections and controls.
Main points about random error correct answers -may represent the influence of those variables
not in the model
-Even if all relevant variables are included in the equation there is still some degree of
randomness in Y that we can not explain with all the Xs, ui captures the randomness
-Ui may represent errors of measurement
-Occams Razor: we prefer to have simple models of stats rather than more complex ones. We try
to ignore the less significant variables which may affect the dependent variable.
Sample Regression Function (SRF) correct answers The estimate of the PRF, finding regression
lines based on a random sample of a population. You can't get beta 1 and 2 based on a sample,
you just get an estimate.
The equation relating the predicted value of the dependent variable to the independent variables,
( typically where the parameter estimates have been obtained by OLS).
the stochastic term
Y ̂ i=β ̂ 1+β ̂ 2 Xi = estimator of E(Y | X_i )
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