Multiple Regression vs. ANOVADate: 09/20/1999 at 12:27:36 From: Frances Van Voorhis Subject: Statistics What is the difference (if any) between multiple regression and ANOVA procedures? Date: 09/27/1999 at 21:47:10 From: Doctor TWE Subject: Re: Statistics Hi Frances. Thanks for asking Dr. Math. My wife teaches statistics at Widener University (at both the undergraduate and graduate levels), so I took the liberty of forwarding your question to her. Here is her response: Regression analysis fits a line to a set of data points. In the case of simple regression, where there is just one independent variable, regression analysis involves fitting a line in two-dimensional space. This line can be easily sketched on two axes on a piece of paper. In multiple regression, where there are k independent variables, the line is in k+1-dimensional space, which conceptually requires k+1 axes. ANOVA (ANalysis Of VAriance) does not involve fitting a line to data. ANOVA tests whether c samples have been drawn from populations with the same mean. For example, suppose four classes of students have been taught using four different teaching techniques. The students' exam scores are then compared. We would like to know whether the average exam scores are essentially the same for all four classes. ANOVA lets us test this hypothesis. (Note that ANOVA is a generalization of the t-test that tests whether the means of two populations are the same by comparing the means of two samples drawn from those populations.) ANOVA works by decomposing the variation in the exam scores into the variation BETWEEN the classes and the variation WITHIN the classes. The variation WITHIN the classes is due simply to chance factors (differences in the students in the class). The variation BETWEEN the classes is due to chance factors and also to differences in the teaching techniques. If the different teaching techniques have no real effect on the exam scores, then both the variation between the classes and the variation within the classes are due just to chance factors, and the two types of variation should be about the same size. If, however, the teaching technique does make a difference in the students' exam scores, then the between variation should be substantially larger than the within variation. ANOVA basically examines the two types of variation to see if they differ in size. I hope that helps. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/ |
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