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September 27, 2007
The Exponential Function (and Logs)
Posted by bparke at 10:54 PM | Comments (0)
The Three-Variables Regression Model
The algebra for the three-variable regression model (two regressors) yields some insights about multiple regression.
Posted by bparke at 10:39 PM | Comments (0)
Elasticities, Logs, and Functional Form
The definitions of elasticity:
A candidate production function:
Another candidate:
Which do economists prefer? Well, economists like to think about elasticities. For a linear model, the elasticity is not constant.
For a log-log model, elasticities are constant (and easier to see).
Posted by bparke at 09:06 AM | Comments (0)
September 25, 2007
Left-Out and Irrelevant Variables
Despite having the wrong handout, low attendance, and a temperature near 90, we had a constructive discussion of left-out and irrelevant variables, capped with a dazzling Monte Carlo demonstration.
Posted by bparke at 09:43 PM | Comments (0)
September 20, 2007
More F Tests
Posted by bparke at 09:42 PM | Comments (0)
September 18, 2007
Multiple Regression & F Tests
Posted by bparke at 09:41 PM | Comments (0)
September 13, 2007
Assumptions
Several important assumptions are needed to justify regression analysis.
We will work with data transformed to deviations from means. This has the effect of suppressing the constant term.
We now derive a fundamental equation that explains a lot about how regressions work.
Accidental arrangements of the error terms (relative to X) cause the estimated slope to deviate from the true value.
The variance of the estimate (previous graphic) is also important. Here is a derivation.
We are in a position to explain the motivation for the following assumptions:
Posted by bparke at 09:35 PM | Comments (0)
September 11, 2007
Confidence Intervals and SHypothesis Tests
Both CI and HT are based on a statistical inference, which is that the variance of the estimator can be inferred from the data even though we have just one observation on the estimator.
There is a close connection between the univariate normal distribution with an estimated mean and the regresion model with estimated parameters.
One-tailed and two-tailed hypothesis tests:
We discussed the difference between regression parameters and correlation/covariance.
Zero correlation does not imply independence:
Correlations/covariance between pairs of variables, in isolation, do not give us the information in regression parameters. For example, going to college basketball games could appear to affect income.
Deriving a confidence interval:
The explanation of precisely what confidence intervals mean would be better for colored chalk.
Posted by bparke at 09:35 PM | Comments (0)
September 06, 2007
What is a good regression?
Should we rank regressions by their R-squareds? How about looking for high t ratios?
The R-squared is defined as follows:
These pictures show generic covariances. The covariance at the top is zero by construction. This is an important property of regression results, and it is prominent in the R-squared derivation above.
Is a high R-squared from a regression of height in centimeters on height in inches better that a more modest R-squared for a regression of weight in pounds on height in inches?
A little review of hypothesis testing from Econ 70:
Posted by bparke at 10:46 PM | Comments (0)
September 04, 2007
Random Variables
Posted by bparke at 11:36 PM | Comments (0)