Law of Large Numbers

The Law of Large Numbers tells us that that the sample mean approaches the mean of the population as we increase the sample size. This simulation investigates the behavior of the sample mean as we change the sample size.

Central Limit Theorem

The Central Limit Theorem states that, for sufficiently large samples, the sample mean is approximately normally distributed, even if the underlying population is not normally distributed (or if we have no idea what the underlying population looks like). This simulation investigates how the distribution of the sample mean is affected by the sample size and the shape of the population distribution.

Confidence Intervals

A confidence interval provides a range of values for the likely location of the true population mean, based on information gathered from a sample.

Hypothesis Testing

Hypothesis testing is a procedure that allows us to form conclusions based on information derived from a sample.

ANOVA

The module presents a simple version of ANOVA (Analysis of Variance), in which we test the null hypothesis that the means of two or more populations are equal.

Joint Distributions

A joint probability distribution describes the simultaneous behavior of two random variables.

Least Squares

Ordinary least squares regression estimates the slope(s) and intercept of a line to best fit data for two (or more) variables by minimizing the sum of the squared distances from the data points to the line.

Sample Distribution of OLS Estimators

The sampling distributions of the OLS estimators and are approximately normal.

The OLS Estimators are Consistent

If the least squares assumptions hold, the OLS estimators, and , converge to the population intercept and slope when the sample is large.

Omitted Variable Bias

Omitted variable bias (OVB) arises when a variable that is i) correlated with the outcome and ii) correlated with one of the included regressors is omitted from the regression model.

Multiple Regression

OLS regression with multiple regressors () estimates the dimensional plane that best fits the data.

Fixed Effects

This module demonstrates how two-way fixed effects impact regression estimates.

Normal Distribution

The normal distribution can be described entirely by its mean and standard deviation. Many natural phenomena can be described by this distribution, and it is possible to test whether a given dataset follows a normal distribution.

Solow Model

Modeling long run economic growth using capital as the driver with shocks.

Measurement Error

This module simulates how coefficients are biased given measurement error in a dependent or independent variable

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