Econ 70 - Fall 2005

Regression Analysis (conclusion)

There are three ways to report regression results: in a table, as an equation with standard errors in parentheses, and as an equation with t ratios in parentheses.

Multiple regression is closely connected to the idea (common in economics) of showing the effects of changing one variable while holding other variables constant. Here we see that beta is the slope of the demand curve, and gamma is the shift that occurs when ads changes by one unit.

Other than a new formula for the degrees of freedom, constructing a confidence interval is a familiar process.

Stata 4

Stata 4 will be the take-home part of your final exam. You will need these links for the data and the variable definitions. For those of you who are bandwidth-impaired, there is a truncated 1000 observation dataset.

Regression Analysis (continued)

Intro to Regression Analysis

Review

Difference in Two Means

Hypoithesis Testing and Confidence Intervals

Problem 9.14

Problem 9.14 (continued)

Stata 3

Stata 3 is due Thursday, December 1.

Hypothesis Testing

The null hypothesis is what we are left with if the evidence is not strong enough to reject it in favor of the alternative hypothesis. We can make two kinds of errors.

A binomial example illustrates the concepts.

A similar Type I / Type II analysis can be conducted for a normal distribution.

Almost all empirical work in economics uses two-tailed alternative hypotheses.

Our ultimate goal is testing hypotheses about regression parameters.

Confidence Intervals for a Sample Proportion

Estimating the probability parameter for a binomial distribution and constructing a confidence interval for that parameter are a classic application of what we have studied so far.

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Second Day of Statistics

The general theory:

My famous boat/net/target explanation for confidence intervals:

The basis for using Student's t distribution to determine the adjustment to the value from the standard normal table that is necessary because the sample variance of the data is used as an estimate of the unknown population variance.

Problem 8.10

Part b asks you to work the problem backwards. In part a you are given the probability level and calculate a confidence interval. In part b you work backward to find that number given the confidence interval.

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First Day of Statistics

On the day after Halloween, we formally started our study of statistics.

]]> Probability theory tells us how the world would look given the true model. Statistics is the process of making inferences about the true model given what we observe.

The Central Limit Theorem is the most important tool in statistics.

The classic problem is asking "What is mu?" Our estimate of mu should have two properties, unbiasedness and efficiency.

Estimators that take a weighted average with unequal weights are unbiased, but not efficient.

Once we have our estimate of mu, we construct a confidence interval that makes a formal probability statement about how accurate our estimate is.

In classical statistics, mu is a fixed, but unknown parameter. The confidence interval is random because the sample mean is random. There is a 95% probability that the random 95% confidence interval includes the fixed, but unknown mu.

The Central Limit Theorem

The Central Limit Theorem can be viewed as the motivation for portfolio diversification.

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One share each of two independent stocks:

Two shares of one stock:

A review of the definition of variance and covariance:

Another view of the Central Limit Theorem is as a way to approximate a binomial distribution for large samples.