# Linear Models

• ### Introduction to Simple Linear Regression

This page explains simple linear regression with an example on muscle strength versus lean body mass.
• ### Linear Regression and Best Fit

This lesson introduces simple linear regression with several Excel spreadsheet examples such as temperature versus cricket chirps, height versus shoe size, and laziness versus amount of TV watched. These activities require class participation.
• ### Analysis Tool: Multiple Linear Regressions

This online calculator allows users to enter 16 observations with up to 4 dependent variables and calculates the regression equation, the fitted values, R-Squared, the F-Statistic, mean, variance, first order serial-correlation, second order serial-correlation, the Durbin-Watson statistic, and the mean absolute errors. It also tests normality and gives the i-th residuals.

• ### Multiple Regression

This resource explains Multiple Regression and concepts associated with it. Key Words: Predicted values; Residuals; Dummy Variables; Interaction Effects; T-Test; Regression Coefficients; Correlation; Partial Correlation; R-Squared; Adjusted R-Squared; Multicollinearity; Variance-Inflation Factors; Transformation; Cook's Distance; Validity; Durbin-Watson Coefficient.
• ### Data Collection: Data Sets from Regression Graphics

The datasets in this collection are in text format, but are also compatible with Arc software from "Regression Graphics." Each set has a title, description, and data table. The software is available in the relation link below.
• ### Social Structure, Race/Ethnicity, and Homocide

As discussed, the murder rates for Blacks in the United States are substantially higher than those for Whites, with Latino murder rates falling in the middle. These differences have existed throughout the 20th and into the 21st century and, with few exceptions, are found in different sections of the United States. Although biological and genetic explanations for racial differences in crime rates, including murder, have been discredited and are no longer accepted by most criminologists, both cultural and structural theories are widespread in the literature on crime and violence. It is also important to remember that Latino is an ethnic rather than a racial classification. The point of this exercise is to examine differences in selected structural positions of Blacks, Whites and Latinos in the United States that may help explain long-standing differences in their murder rates.
• ### Data Collection: Time Series Data Library

This collection of datasets covers many application areas, but are all for time series analysis. The data are in text format.
• ### 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.
• ### Intuitive Biostatistics: Choosing a Statistical Test

This page provides a table for selecting an appropriate statistical method based on type of data and what information is desired from the data. It also compares parametric and nonparametric tests, one-sided and two-sided p-values, paired and unpaired tests, Fisher's test and the Chi-square test, and regression and correlation. It comes from Chapter 37 of the textbook, "Intuitive Biostatistics".
• ### IDEAL: Probability Definitions

This module discusses the probability of an event and relative frequency. The applet shows how empirical probability converges to theoretical probability as the sample size increases. The follow-up example includes an applet that simulates drawing differently colored balls from an urn.