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# Statistics Dictionary

To see a definition, select a term from the dropdown text box below. The statistics dictionary will display the definition, plus links to related web pages.

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### Regression

In a cause and effect relationship, the
**independent variable** is the cause, and the
**dependent variable** is the effect.
**Least squares linear regression** is a method
for predicting the value of a dependent variable *Y*,
based on the value of an independent variable
*X*.

Linear regression finds the straight line, called the
**least squares regression line** or LSRL, that
best represents observations in a
bivariate
data set. Suppose *Y* is a dependent variable,
and *X* is an independent variable. Then, the equation
for the regression line would be:

ŷ = b_{0} + b_{1}x

where b_{0} is a constant,
b_{1} is the regression coefficient,
x is the value of the independent variable, and ŷ is the
*predicted* value of the dependent variable.

Normally, you will
use a computational tool - a software package (e.g., Excel) or a graphing calculator -
to find b_{0} and b_{1}. You enter the
*X* and *Y* values into your program or calculator,
and the tool solves for each parameter.

In the unlikely event that you find yourself on a desert island
without a computer or a graphing calculator, you can solve for
b_{0} and b_{1} "by hand". Here are the
equations.

b_{1} = Σ
[ (x_{i} - x)(y_{i} - y) ] / Σ
[ (x_{i} - x)^{2}]

and

b_{0} = y - b_{1} * x

where b_{0} is the constant in the regression equation,
b_{1} is the regression coefficient,
x_{i} is the *X* value of observation *i*,
y_{i} is the *Y* value of observation *i*,
and x and y
are the means of *X* and *Y*, respectively.

See also: | AP Statistics Tutorial: Least Squares Linear Regression |