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Basic Econometrics

- Literally defined as economic measurement
- Econometrics may be defined as the social science

in which the tools of economic theory,

mathematics, and statistical inference are

applied to the analysis of economic phenomena.

Arthur S. Goldberger, 1964

Ordinary Least Squares

- Ordinary Least Squares a statistical method that

chooses the regression line by minimizing the

squared distance between the points and the line. - i.e. minimize the sum of S, where S ?e2
- where e the distance between the line and the

point, or the error term. - Error term (e) random, included because we do

not expect a perfect relationship. - Why not sum the errors? Generally equals zero
- Why not take the absolute value of the errors? We

wish to emphasize large errors.

Source of Error

- Omitted variables
- Measurement error
- Incorrect functional form

Univariate Analysis

- Y a bX Where
- Y The Dependent Variable, or what you are

trying to explain (or predict). - X The Independent Variable, or what you believe

explains Y. - a the y-intercept or constant term.
- b the slope or coefficient

The t-statistic

- To evaluate the quality of our slope coefficient

we refer to the - t-statistic.
- T-statistic slope coefficient / standard error
- Standard error - estimated standard deviation of

the coefficient - Rule of thumb T-stat gt 2
- Why? We want to know whether or not the

coefficient is statistically different from zero. - The t-statistic is used to test the null

hypothesis (H0) that the coefficient is equal to

zero. The alternative hypothesis (HA) is that the

coefficient is different than zero.

The slope coefficient

- How do we interpret the slope coefficient?
- Example
- Wins -0.1508 0.0063PTS per game
- Each additional one point per game results in a

0.0063 increase in winning percentage. - How many wins is this? 0.513 over an 82 game

season. - Is this the truth? We never know the truth, we

are simply attempting to derive estimates. - Is this a good estimate? Clearly points alone

do not explain wins.

The constant term

- How do we interpret the constant term?
- The constant term must be included in the

regression, or else we are forcing the regression

line through zero. - The constant term is used to impose a zero mean

for the error term, hence it acts as a garbage

collector. In other words, it captures all the

factors not explicitly utilized in the equation. - The constant term is theoretically the value of Y

when X is zero. Frequently this is outside the

range of possibility, and therefore the constant

term should not be interpreted.

Multivariate Analysis

- Introducing the idea of ceteris paribus.
- One cannot impose ceteris paribus unless all

relevant variables are included in the model. - Wins a b(ORB)
- As illustrated earlier, the estimated impact of

offensive rebounds (ORB) on wins is negative. - In other words, b lt 0
- Wins c d(Missed Shots)
- The value of d lt 0
- ORB e f(Missed Shots)
- the value of f gt 0
- In other words, missed shots and offensive

rebounds are positively related. So when we

estimate wins as a function of offensive

rebounds, we are simply picking up the

relationship between wins and missed shots.

R-squared

- How do we know how accurate our equation is?
- R-squared Explained Sum of Squares / Total Sum

of Squares - Total sum of squares Sum of the squared

difference between the actual Y and the mean of

Y, or, - TSS ?(Yi - mean of Y)2
- Explained sum of squares Sum of the squared

differences between the predicted Y and the mean

of Y, or, - ESS ?(Y - mean of Y)2
- Residual sum of squares Sum of the squared

differences between the actual Y and the

predicted Y, or, - RSS ? e2
- The coefficient of determination Ratio of the

explained sum of squares to the total sum of

squares. (Provide example) - R2 ESS/TSS R2 1 - RSS/TSS
- 1 - ? e2 / ? (Yi - mean of Y)2

Adjusted R-Squared

- Adding any independent variable will increase R2.

To combat this problem,we often report the

adjusted R2. - Adjusted R2 1 - RSS/(n-K-1) / TSS/(n-1)
- where n observations
- K number of coefficients

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