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Chapter 4 Econometrics
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1) When the estimated slope coefficient in the simple regression model, B^1, is zero, then
R2 = 0.
R^2
ESS/TSS
The standard error of regression (SER) is defined as follows
1/n-2(SUM u^i^2)
TSS=
ESS+SSR
Binary variables
can only take on two values
The least squares assumptions:
1 The conditional distribution of ui given Xi has a mean of zero.
2 (Xi, Yi), i = 1,..., n are independently and identically distributed.
3 Large outliers are unlikely.
The reason why estimators have a sampling distribution is that
the values of the explanatory variable and the error term differ across samples.
In the simple linear regression model, the regression slope
indicates by how many units Y increases, given a one unit increase in X.
The OLS estimator is derived by
minimizing the sum of squared residuals.
Interpreting the intercept in a sample regression function is
reasonable if your sample contains values of Xi around the origin.
The variance of Yi is given by
var(Xi) + var(ui).
The sample average of the OLS residuals is
zero.
The OLS residuals, u^i, are defined as follows:
Yi-Y^i
The slope estimator, β1, has a smaller standard error, other things equal, if
there is more variation in the explanatory variable, X.
The regression R^2 is a measure of
the goodness of fit of your regression line.
The sample regression line estimated by OLS
will always run through the point (Xbar,Ybar )
The OLS residuals can be calculated by
subtracting the fitted values from the actual values.
In the simple linear regression model Yi = β0 + β1Xi + ui,
β0 + β1Xi represents the population regression function.
To obtain the slope estimator using the least squares principle, you divide the
sample covariance of X and Y by the sample variance of X.
To decide whether or not the slope coefficient is large or small,
you should analyze the economic importance of a given increase in X.
E(uiXi) = 0 says that
the conditional distribution of the error given the explanatory variable has a zero mean.
In the linear regression model, Yi = β0 + β1Xi + ui, β0 + β1Xi is referred to as
the population regression function.
The OLS residuals, u^i, are sample counterparts of the population
errors
Changing the units of measurement, e.g. measuring testscores in 100s, will do all of the following EXCEPT for changing the
interpretation of the effect that a change in X has on the change in Y
To decide whether the slope coefficient indicates a "large" effect of X on Y, you look at the
A) size of the slope coefficient
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