Multivariate Quantitative Relationships

  • This Flash applet provides an introduction to simple linear regression for introductory statistics students. It combines a brief narrated animation with an interactive scatterplot function. Students are able to place points on the scatterplot by clicking with a mouse or typing X-Y coordinates. Students use these points to learn about the best fit line by placing a guess on the plot and comparing it with the least squares line. Students also learn about the value of the correlation coefficent and points that would be considered outliers. Students may also specify a value of x (within the range of the data) and obtain the resulting predicted value.
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  • This is a virtual spinner applet, which allows you to change spinner regions and the number of spins. It records the results and displays the data in a histogram.
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  • A "12 page" tutorial that explores the liner models via excel spreadsheets. The learning module leads the user through various aspects of linear modeling. This tutorial includes a worksheet that allows students to vary the scatter (or noise) level, by adjusting the scroll bar or by clicking on the arrows, to see how the slope and intercept of line respond to the addition of scatter to the data, while monitoring the value of r^2.

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  • This correlation and regression example compares performance on reading comprehension questions to performace on the SAT. It also compares those who read the passage referred to by the questions to those who did not. Exercise questions and answers are also provided.
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  • As described in the web page itself: "This document was prepared as an illustration of the use of both t tests and correlation/regression analysis in drawing conclusions from data in an actual study." The study compares athletic performance of swimmers that are optimists vs. pessimists.
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  • 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.

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  • Residual plots and other diagnostics are important to deciding whether or not linear regression is appropriate for a set of data. Many students might believe that if the correlation coefficient is strong enough, these diagnostic checks are not important. The data set included in this activity was created to lure students into a situation that looks on the surface to be appropriate for the use of linear regression but is instead based (loosely) on a quadratic function. Key words: regression, residuals
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  • 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.

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  • The program DistCalc calculates probabilities and critical values for the most important distributions. The purpose of this program is to show the concept of critical values and the replacement of printed distribution tables. The Distribution Calculator offers calculations for the normal distribution, the t distribution, the chi-square distribution, and the F distribution.

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  • 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.

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