2.) Ordinary Least Squares

Question 1

Why use Ordinary Least Squares?

Answer 1

1. ) OLS is relatively easy to use.
2. ) The goal of minimizing sum of error squared is quite appropriate from a theoretical point of view
3. ) OLS estimates have a number of useful characteristics

Question 2

Ordinary Least Squares (OLS)

Answer 2

is a regression estimation technique that calculates the estimated slope coefficients so as to minimize the sum of the squared residuals

Question 3

An estimator is …

Answer 3

a mathematical technique that is applied to a sample of data to produce real-world numerical estimates of the true population regression coefficients (or parameters). So, OLS is an estimator, and an estimated slope coefficient produced by OLS is an estimated.

Question 4

What are the three reasons for using OLS?

Answer 4

1. ) It is the simplest of all econometric estimation techniques.
2. ) Minimizing the summed, squared residuals is a reasonable goal for an estimation technique.
3. ) Has the following two useful characteristics.
   a. ) The sum of the residuals is exactly zero.
   b. ) OLS can be show to be the “best” estimator possible under a set of specific assumptions

Question 5

K =

Answer 5

of independent variables

Question 6

i =

Answer 6

goes from 1 to N and indicates the ith observation of independent variable

Question 7

the biggest difference btw a single-independent-variable regression model and a multivariate regression model is

Answer 7

the interpretations of the latter’s slope coefficients, often called partial regression coefficients, are defined to allow a researcher to distinguish the impact of one variable from that of other independent variables.

Question 8

You should always include beta naught in a regression equation,…

Answer 8

but you should not rely on estimates of beta naught for inference

Question 9

Total Sum of Squares

Answer 9

is the squared variations of Y around its mean as a measure of the amount of variation to be explained by the regression.

Question 10

For OLS, the total sum of squares has two components….

Answer 10

1. ) Variation that can be explained by the regression

2. ) Variation that cannot

Question 11

TSS = ESS + RSS

Answer 11

this is usually called the decomposition of variance

Question 12

Decomposition of the variance in Y

Answer 12

The variation of Y around its mean (Y - Yavg) can be decomposed into two parts:

1. ) (Yobs - Yavg) = the difference between the estimated value of Y(Yhat) and the mean value of Y (Yavg).
2. ) (Yi-Yhat) = the difference between the actual value of Y and the estimated value of Y.

Question 13

Explained Sum of Squares (ESS) =

Answer 13

Measures the amount of the squared deviation of Yi from its mean that is explained by the regression line. It is attributable to the fitted regression line.

Question 14

Residual Sum of Squares

Answer 14

This is the unexplained portion of TSS (that is, unexplained in an empirical sense by the estimated regression line)

Question 15

The smaller the RSS is relative to the TSS…

Answer 15

the better the estimated regression line fits the data.

Question 16

OLS is the estimating technique that…

Answer 16

minimizes the RSS and therefore maximizes the ESS for a given TSS

Question 17

Once the computer estimates have been produced, what are some questions that an econometrician should ask…

Answer 17

1. ) Is the equation supported by sound theory?
2. ) How well does the estimated regression fit the data?
3. ) Is the data set reasonably large and accurate?
4. ) Is OLS the best estimator to be used for this equation?
5. ) How well do the estimated coefficients correspond to the expectations developed by the researcher before the data were collected?
6. ) Are all the obviously important variables included in the equation?
7. ) Has the most theoretically logical functional form been used?
8. ) Does the regression appear to be free of major econometric problems?

Question 18

R^2

Answer 18

is the ratio of the explained sum of squares over the

Question 19

A major problem with R^2 is…

Answer 19

that adding another independent variable to a particular equation can never decrease R^2

Question 20

Degrees of freedom an also be understood as…

Answer 20

the excess numbers of observations (N) over the number of coefficients (concluding the intercept) estimated (K + 1)

Question 21

R-bar-squared

Answer 21

which is R^2 adjusted for degrees of freedom

Question 22

When is R^2 of little help?

Answer 22

If we’re trying to meaningfully explain If adding a variable to an equation improves our ability to explain the dependent variable.

Question 23

R-squared-bar measures…

Answer 23

the percentage of the variation of Y around its mean that is explained by the regression equation, adjusted for degrees of freedom.

Question 24

R-squared bar can be used to…

Answer 24

compare the fits of equations with the same dependent variable and different numbers of independent variables. Because of this property, most researchers automatically use R-squared-bar in stead of R-squared when evaluating the fit of their estimated regression equations.

Question 25

Adding a variable can’t change TSS, but…

Answer 25

but in most cases the added variable will reduce RSS, so R^2 will rise

Question 26

Degrees of freedom, or the…

Answer 26

excess of the number of observations (N) over the number of coefficients (including the intercept) estimated (K + 1).

Question 27

The variation of Y around its mean can be decomposed into two parts…

Answer 27

1. ) The different btw the estimated value of Y and the mean value of Y
2. ) The difference between the actual value of Y and the estimated value of Y

Question 28

OLS selects those estimates of beta naught and beta one that …

Answer 28

minimize the squared residuals, summed over all the sample data points.

Question 29

Ordinary Least Squares (OLS) is a regression estimation technique that calculates…

Answer 29

betas so as to minimize the sum of the squared residuals.