# Calculus required

• ### *Using an Applet to Demonstrate Sampling Distributions of Regression Coefficients

This visualization activity combines student data collection with the use of an applet to enhance the understanding of the distributions of slope and intercept in simple linear regression models. The applet simulates a linear regression plot and the corresponding intercept and slope histograms. The program allows the user to change settings such as slope, standard deviation, sample size, and more. Students will then see theoretical distributions of the slope and intercept and how they compare to the histograms generated by the simulated linear regression lines.
• ### *Using an Applet to Demonstrate a Sampling Distribution

This in-class demonstration combines real world data collection with the use of the applet to enhance the understanding of sampling distribution. Students will work in groups to determine the average date of their 30 coins. In turn, they will report their mean to the instructor, who will record these. The instructor can then create a histogram based on their sample means and explain that they have created a sampling distribution. Afterwards, the applet can be used to demonstrate properties of the sampling distribution. The idea here is that students will remember what they physically did to create the histogram and, therefore, have a better understanding of sampling distributions.
• ### A Brief Introduction to Bayesian Statistics

This pdf text file gives a short introduction to the methods of Bayesian inference. It gives a simple example that deals with jumping a paper frog. The topics listed in this document include: An example, comparison of frequentist and Bayesian methods, credible vs. confidence intervals, choice of prior and its effect on the posterior distribution.
• ### Regression, Prediction, and Model Building

This tutorial explains the theory and use of Multiple Regression and demonstrates it with an example on SAT scores and GPA. Data is given as well as SPSS and Minitab code.
• ### Student's t-Test for Matched Pairs

This tutorial explains the theory and use of Student's t-test for matched pairs and demonstrates it with an example on project quality. Data is given as well as SPSS and Minitab code.
• ### Descriptive Statistics, Measures of Central Tendency, and Dispersion

This tutorial describes various measures of central tendency, their theory and use, and demonstrates them with an example on final exam scores. Data is given as well as SPSS and Minitab code. Key Words: Mean; Median; Mode; Variance; Standard Deviation.
• ### Introduction to Radial Basis Function Networks

This article introduces Radial Basis Function (RBF) networks. These networks rely heavily on regression analysis techniques. Topics include Nonparametric Regression, Classification and Time Series Prediction, Linear Models, Least Squares, Model Selection Criteria, Ridge Regression, and Forward Selection.
• ### A Brief Introduction to Probability and Statistics

This online textbook covers the following probability and statistics topics: Independence; Venn Diagrams; Bayes's Theorem; Counting; Binomial Expansion; Binomial Distribution; Continuous Distributions; Infinitesimals in Probability; Averaging; Variance; Gaussian Distribution; Random Walks; Correlation; Causation; Linear Regression; Unbiased Estimators; Hypothesis Testing; Shape of the Distribution; Variance of Mean Differences.
• ### Statistics and Probability Tutorial

This tutorial provides a basic introduction to many topics in statistics and probability. Topics include: Sets and subsets, Statistical experiments, Counting, Basic probability rules, Bayes' theorem, Probability distributions, Discrete vs. Continuous, Binomial, Negative Binomial, Hypergeometric, Multinomial, Poisson, Normal, Sampling theory, Central tendency, Variability, Sampling distributions, t Distribution, Chi-Square Distribution, F Distribution, Estimation problems, Hypothesis testing, Power, Survey sampling, Simple random samples, Stratified samples, Cluster samples, Sample size.
• ### Understanding the Least-Squares Regression Line

This applet allows students to explore three methods for measuring "goodness of fit" of a linear model. Users can manipulate both the data and the regression line to see changes in the square error, the absolute error, and the shortest distance from the data point to the regression line.