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# Regression

• ### Random Number Generator

This random number generator produces a data table with up to 10 columns and up to 2500 rows. For random integers, users must specify the data range. For data from a Normal (Gaussian) distribution, users specify mean and standard deviation.

• ### Benford's Law Part 2 - The 80/20 Rule or Pareto Principle

This page explores Benford's law and the Pareto Principle (or 80/20 rule). Benford's law may also have a wider meaning if the digits it evaluates are considered ranks or places. The digit's probability of occurring could be considered the relative share of total winnings for each place (1st through 9th). In other words, 1st place would win 30.1%, 2nd place 17.6%, 3rd 12.5%,... 9th place 4.6% of the available rewards. The normalized Benford curve could be used as a model for ranked data such as the wealth of individuals in a country. To determine if the Benford model gives results similar to those of the Pareto principle we use the normalized Benford equation in a computer program.
• ### The Awesome Power of Twenty Questions

This page shows how elements of a systems can be eliminated as causes in problem troubleshooting. The principles of twenty questions are frequently used in the business world to conduct computerized searches of massive data bases. These are called a binary searches and are one of the fastest search methods available. To conduct binary searches, data must be sorted in order or alphabetized. The computer determines which half of the list contains the item. The half containing the item is divided in half again and the process repeated until the item is found or the list can no longer be divided. Problem solvers should avoid focusing on the cause and instead ask which elements of the system can be eliminated as causes.
• ### **The Central Limit Theorem - How to Tame Wild Populations

Using a parameter it's possible to represent a property of an entire population with a single number instead of millions of individual data points. There are a number of possible parameters to choose from such as the median, mode, or interquartile range. Each is calculated in a different manner and illuminates the data from a different point of view. The mean is one of the most useful and widely used and helps us understand populations. A population is simulated by generating 10,000 floating point random numbers between 0 and 10. Sample means are displayed in histograms and analyzed.
• ### Analysis Tool: Linear Regression Applet

This applet allows a person to add up to 50 points onto its green viewing screen. After each point is added by clicking on the screen with the mouse, a red line will appear. This red line represents a line passing through (Average x, Average y) with a slope that can be altered by clicking the Left or Right buttons. The slope of this line may also be changed by dragging the mouse either right or left. By clicking on Show Best Fit, a blue best fit line will be calculated by the computer.

• ### Mackichan software

A mathematical word processor that includes an easy-to-use computer algebra system (MuPad). Products include Scientific Wokplace, Scientific Word, Scientific Notebook, and MuPad Pro. Student version are available.

• ### Leverage Effect in Regression Simulation

This program visualizes the effects of outliers to regression lines. The user may pick up a point with the mouse and move it across the chart. The resulting regression line is automatically adjusted after each movement, showing the effect in an immediate and impressive way. The program Leverage allows one to experiment with the leverage effect. You can create a random sample of data noisy points on a line. Dragging one of the points away from the regression line immediately shows the effect, as the regression line is recalculated and moves according to the current data set. Not online: user has to download the program.

• ### Error Surface of Linear Regression

This program has been written to explore the relationship between the data points and the error surface of the regression problem. On one hand you can learn how to represent a line in two different spaces ({x,y} and {k,d}), and on the other hand you see that solving the regression problem is nothing else than finding the minimum in the error surface.

• ### Examples and Their Data Sets

Each dataset in this collection includes description of the study, description of the data file, statistical topic covered, and reference. Topics addressed include: correlation, one-way ANOVA, Bonferroni multiple comparison procedure, regression (simple, multiple, and loglinear), chi-square, and the t-test.
• ### Analysis Tool: Rossman/Chance JAVA Applet Collection

A collection of applets addressing data analysis, sampling distribution simulations, and probability and inference. Some can be used individually, though others require context from the textbook.