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Exploring Bivariate and Categorical Data
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Exploring Categorical Data: Frequency Tables
Exploring Bivariate Data
Exploring Data
The Exploring Data Web site contains three great activities for exploring bivariate data. All three contain student worksheets. "The Challenger Disaster" is a good introduction to scatterplots, giving a brief background to the shuttle disaster and providing the data collected prior to the disaster. The famous "Anscombe Data Set" gives proof of the need to always look at a data set first; and "Using a Scatterplot to Find a Friend" provides a fun activity that uses current movies as the basis of the activity.
Mrs. Smart's AP Statistics Assignments
Joyce Smart, from Logan High School in Logan, Utah, has several activities for exploring bivariate data. Among the most useful are "Leonardo," where students investigate relationships in the human body; "Skittleium," where students track the decay of a population of Skittles candy; and "Barbie Bungee," where students use linear regression equations to predict the number of rubber bands necessary to keep Barbie from hitting her head as she jumps from great heights.
Mrs. Smart's AP Statistics Assignments
AP Statistics Activities
Paul Myers' site has an activity that uses Monopoly to explore regression. Students explore whether or not there is a relationship between property cost and distance from the 'GO' square.
AP Statistics Activities
Computing and Analyzing Regression Lines
Daren Starnes' site has step-by-step instructions for using your TI-83 graphing calculator to enter data, construct scatterplots, compute regression equations, and construct residual plots.
Computing and Analyzing Regression Lines
Linear Regression (and Best Fit)
Amar Patel's Web site contains a detailed lesson plan for exploring relationships between two variables. Students work through data sets and activities to gain a deeper understanding of the topic.
Linear Regression (and Best Fit)
Guessing Correlations
The Correlation Game is a java applet that lets students practice guessing the correlation of randomly generated scatterplots. Instructors can set up a group for classroom competitions.
Guessing Correlations
Regression by Eye
This Java applet from the Rice Virtual Lab in Statistics produces a random scatterplot. The user can then guess the correlation coefficient (from among 5 given values) and compare with the real correlation coefficient, estimate the regression line with the mean squared error shown, and draw the regression line to see the closeness of their estimate.
Regression by Eye
Components of r
Another applet from the Rice Virtual Lab in Statistics, Components of r allows the user to independently manipulate the slope, standard error of the estimate, and standard deviation of X to see their effects on the scatterplot and on r for a given bivariate set of data.
Components of r
Transformations
A third applet from the Rice Virtual Lab in Statistics demonstrates how transformations (including logs, squares, and square roots) on one or both of the variables of a bivariate dataset affect the relationship between two variables.
Transformations
r-Square and Residuals
This java applet by Robert C. delMas allows the user to step through the calculation of the least squares regression line. It highlights the relationship between residuals and r-squared.
r-Square and Residuals
Regression Applet
R. Webster West, from the University of South Carolina, provides a data set and resulting regression line and then lets the user add another point to compare the new regression, including the added point, to the old one. The use of this applet allows the user to clearly see which points are influential to a linear model.
Regression Applet
SticiGui: Scatterplots and Association
Philip B. Stark, from the University of California at Berkeley, has designed a java applet that provides for an exploration of correlation, linear regression, and residual plots for four datasets. Additionally, the user is able to add data values to see the changes that occur.
SticiGui: Scatterplots and Association
STAR Library
The STAR Library site contains three activities to explore correlation and regression: "Regression on the Rebound," "Regression -- Residuals -- Why?" and "What is the Shelf Life?" (Follow the link that says, "Click here to view a list of all activities published in the STAR Library.")
The STAR Library
Running to Conclusions
This site contains a lesson on the running of the mile by Ed Malczewski that explores the process for finding the best-fitting exponential curve to sets of data.
Running to Conclusions
AP Statistics at BB&N School
Al Coons' site contains investigations or worksheets for "Understanding the Correlation Coefficient" and "Understanding r-squared."
AP Statistics at BB&N School
Exploring Categorical Data: Frequency Tables
Frequency Distributions
A discussion of frequency distributions can be found at this site for Introductory Statistics: Concepts, Models, and Applications by David W. Stockburger.
Frequency Distributions
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