# 2.) Ordinary Least Squares Flashcards

1
Q

Why use Ordinary Least Squares?

A
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
2
Q

Ordinary Least Squares (OLS)

A

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

3
Q

An estimator is …

A

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.

4
Q

What are the three reasons for using OLS?

A
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
5
Q

K =

A

of independent variables

6
Q

i =

A

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

7
Q

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

A

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.

8
Q

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

A

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

9
Q

Total Sum of Squares

A

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

10
Q

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

A
1. ) Variation that can be explained by the regression

2. ) Variation that cannot

11
Q

TSS = ESS + RSS

A

this is usually called the decomposition of variance

12
Q

Decomposition of the variance in Y

A

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.
13
Q

Explained Sum of Squares (ESS) =

A

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.

14
Q

Residual Sum of Squares

A

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

15
Q

The smaller the RSS is relative to the TSS…

A

the better the estimated regression line fits the data.

16
Q

OLS is the estimating technique that…

A

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

17
Q

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

A
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?
18
Q

R^2

A

is the ratio of the explained sum of squares over the

19
Q

A major problem with R^2 is…

A

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

20
Q

Degrees of freedom an also be understood as…

A

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

21
Q

R-bar-squared

A

which is R^2 adjusted for degrees of freedom

22
Q

When is R^2 of little help?

A

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

23
Q

R-squared-bar measures…

A

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

24
Q

R-squared bar can be used to…

A

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.

25
Q

Adding a variable can’t change TSS, but…

A

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

26
Q

Degrees of freedom, or the…

A

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

27
Q

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

A
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
28
Q

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

A

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

29
Q

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

A

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