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### Multiple Regression vs. ANOVA

```
Date: 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
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/
```
Associated Topics:
High School Probability

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