In this R script, we test to see if a continuously distributed random variable is normally distributed. Typically, empirical observations need not follow a specific distribution, so we need to conduct statistical test to see what is the most likely distribution. Experimentally, we sample from an exponential and normal distribution and perform the Shapiro-Wilk test (useful for low samples - KS test for large samples) to test for normality.

A demonstration of Step-Wise regression.

In this R script, we illustrate the heterogeneity of the posterior distribution using a Dirichlet prior for the multinomial distribution. We display Bayesian conjugacy plots that display the variability of prior and posterior distributions in the form of a contour plot.

In this R script, we explore the finite difference equation known as the logistic equation. We compute the trajectories for various parameter values of r and plot the steady states as a function of r and plot the last 400 of the 1200 time points. The result is a bifurcation map that displays a period-doubling bifurcation along with a region of chaotic oscillations (unpredictable).

Analysis pipeline and preliminary results

In this R script, we conjecture if the population variance is greater than the hypothesized population variance using the sample standard and critical chi-square value. If the p-value is below a threshold, we reject the null hypothesis and the population variance is indeed greater than the hypothesized variance. Results are useful when comparing samples and making inferences about the population variances before performing statistical tests on the measures of central tendency.

In this R script, we explore the methods to estimate the population variance using the chi-square distribution and interval estimation. Results can be applied to a given data variable where the population variance is unknown, but the sample standard deviation can be computed.

In this Rscript, we illustrate the connection between the Incomplete Beta Function (used in the Beta probability distribution) and how it is related to the Gamma function.

This document provides a rough overview of the statistical method - Linear Regression. It used code examples, and explains the logic behind everything.