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,ECONOMETRICS TOPICS
Chapter 1: An Overview of Regression Analysis
What is econometrics?
Econometrics: economic measurement
Uses of econometrics:
1. Describing economic reality
2. Testing hypothesis about economic theory
3. Forecasting future economic activity
Alternative economic approaches
Steps necessary for any kind of quantitative research:
1. Specifying the models or relationships to be studied
2. Collecting the data needed to quantify the models
3. Quantifying the models with the data
Single-equation linear regression analysis is one particular economic
approach that is the focus of this book.
What is regression analysis?
Dependent variables, independent variables, and causality
Regression analysis: a statistical technique that attempts to explain
movements in one variable, the dependent variable, as a function of
movements in a set of other variables, called the independent (or
explanatory) variables, through the quantification of a single equation.
A regression result, no matter how statistically significant, cannot prove
causality. All regression analysis can do is test whether a significant
quantitative relationship exists.
Single-equation linear models
Betas: the coefficients that determine the coordinates of the straight line at
any point.
Beta-null: the constant or intercept term; it indicates the value of Y when
X equals zero.
Beta-one: the slope coefficient; it indicates the amount that Y will change
when X increases by one unit.
An equation is linear in the variables if plotting the function in terms of X
and Y generates a straight line.
An equation is linear in the coefficients only if the coefficients appear in
the simplest form – they are not raised to any powers are not multiplied or
divided by other coefficients, and do not themselves include some sort of
function.
The stochastic error term
Stochastic error term: a term that is added to a regression equation to
introduce all of the variation in Y that cannot be explained by the included
X’s.
-1-
, The deterministic component: B0 + B1X; can be thought of as the expected
value of Y given X, the mean value of the Ys associated with a particular
value of X.
The stochastic error term must be present in a regression equation because
there are at least four sources of variation in Y other than the variation in
the included Xs:
1. Many minor influences on Y are omitted from the equation (for
example, because data are unavailable).
2. It is virtually impossible to avoid some sort of measurement
error in at least one of the equation’s variables.
3. The underlying theoretical equation might have a different
functional form than the one chosen for the regression. For
example, the underlying equation might be nonlinear in the
variables for a linear regression.
4. All attempts to generalize human behavior must contain at least
some amount of unpredictable or purely random variation.
Extending the notation
The meaning of the regression coefficient beta-one: the impact of a one
unit increase in X-one on the dependent variable Y, holding constant the
other included independent variables.
Multivariate regression coefficients: serve to isolate the impact on Y of a
change in one variable from the impact on y of the changes in the other
variables.
The estimated regression equation
Estimated regression equation: a quantified version of the theoretical regression
equation
Estimated regression coefficients: empirical best guesses of the true regression
coefficients and are obtained from a sample of the Xs and Ys; denoted by beta-
hats
A simple example of regression analysis
Using regression to explain housing prices
Chapter 2: Ordinary Least Squares
Estimating single-independent-variable models with OLS
Ordinary least squares (OLS): a regression estimation technique that calculates
the beta-hats so as to minimize the sum of the squared residuals.
Why use ordinary least squares?
1. OLS is relatively easy to use.
2. The goal of minimizing the sum of the squared residuals is quite
appropriate fro a theoretical point of view.
3. OLS estimates have a number of useful characteristics:
-2-
EXAM PACK
2023
QUESTIONS WITH ANSWERS
EMAIL:
,ESC3706
EXAM PACK
2023
LATEST QUESTIONS AND ANSWERS
FOR ASSIGNMENTS AND EXAM PACKS,
EMAIL:
,ECONOMETRICS TOPICS
Chapter 1: An Overview of Regression Analysis
What is econometrics?
Econometrics: economic measurement
Uses of econometrics:
1. Describing economic reality
2. Testing hypothesis about economic theory
3. Forecasting future economic activity
Alternative economic approaches
Steps necessary for any kind of quantitative research:
1. Specifying the models or relationships to be studied
2. Collecting the data needed to quantify the models
3. Quantifying the models with the data
Single-equation linear regression analysis is one particular economic
approach that is the focus of this book.
What is regression analysis?
Dependent variables, independent variables, and causality
Regression analysis: a statistical technique that attempts to explain
movements in one variable, the dependent variable, as a function of
movements in a set of other variables, called the independent (or
explanatory) variables, through the quantification of a single equation.
A regression result, no matter how statistically significant, cannot prove
causality. All regression analysis can do is test whether a significant
quantitative relationship exists.
Single-equation linear models
Betas: the coefficients that determine the coordinates of the straight line at
any point.
Beta-null: the constant or intercept term; it indicates the value of Y when
X equals zero.
Beta-one: the slope coefficient; it indicates the amount that Y will change
when X increases by one unit.
An equation is linear in the variables if plotting the function in terms of X
and Y generates a straight line.
An equation is linear in the coefficients only if the coefficients appear in
the simplest form – they are not raised to any powers are not multiplied or
divided by other coefficients, and do not themselves include some sort of
function.
The stochastic error term
Stochastic error term: a term that is added to a regression equation to
introduce all of the variation in Y that cannot be explained by the included
X’s.
-1-
, The deterministic component: B0 + B1X; can be thought of as the expected
value of Y given X, the mean value of the Ys associated with a particular
value of X.
The stochastic error term must be present in a regression equation because
there are at least four sources of variation in Y other than the variation in
the included Xs:
1. Many minor influences on Y are omitted from the equation (for
example, because data are unavailable).
2. It is virtually impossible to avoid some sort of measurement
error in at least one of the equation’s variables.
3. The underlying theoretical equation might have a different
functional form than the one chosen for the regression. For
example, the underlying equation might be nonlinear in the
variables for a linear regression.
4. All attempts to generalize human behavior must contain at least
some amount of unpredictable or purely random variation.
Extending the notation
The meaning of the regression coefficient beta-one: the impact of a one
unit increase in X-one on the dependent variable Y, holding constant the
other included independent variables.
Multivariate regression coefficients: serve to isolate the impact on Y of a
change in one variable from the impact on y of the changes in the other
variables.
The estimated regression equation
Estimated regression equation: a quantified version of the theoretical regression
equation
Estimated regression coefficients: empirical best guesses of the true regression
coefficients and are obtained from a sample of the Xs and Ys; denoted by beta-
hats
A simple example of regression analysis
Using regression to explain housing prices
Chapter 2: Ordinary Least Squares
Estimating single-independent-variable models with OLS
Ordinary least squares (OLS): a regression estimation technique that calculates
the beta-hats so as to minimize the sum of the squared residuals.
Why use ordinary least squares?
1. OLS is relatively easy to use.
2. The goal of minimizing the sum of the squared residuals is quite
appropriate fro a theoretical point of view.
3. OLS estimates have a number of useful characteristics:
-2-
