# Linear Regression

A classic statistical problem is to try to determine
the relationship between a random

variable *Y.* and an independent
variable *x*.
For example, we might consider height and weight of a sample of adults.

Linear regression attempts to explain this relationship by fitting a curve
to the data.

The linear regression model postulates that

*Y= b*_{0}+b_{1} x_{1}+ ... +b_{n}x_{n}+ e,
where the *x*_{i} are independent variables and the "residual" *e *is a random
variable with mean zero.
In this applet, we consider the simplest example of fitting a straight line:

*Y= a+bx+e.* The coefficients *a* and *b* are
determined by the condition that the sum of the square residuals is as small
as possible.
### The applet:

This applets let you mark the locations of order
pairs *(x, Y), * on the left screen and then determines the equation

of the
regression line and graphs it.
The applet will also show confidence bands for means of *y*
corresponding to a given *x*,
and prediction bands for future values of *y* corresponding to
a given value *x*.
### References:

Regression is discussed in most introductory statistics texts.
## Source Code

This applet uses the Danby package in additon to the following
java files:

This applet was written by
Charles Stanton