# Regression

Description of regression

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## Definitions

Explanatory Value - The value that is normally labelled "X", and is chosen by the experimenter, also known as the independant variable

Response Variable - The value that is normally labelled "Y" and is dependant on the explanatory value, also known as the dependant variable

Scatter Diagram - The graph of the pairs of the 2 variables. The explanatory value is plotted on the bottom, and the response value down the side

Straight line law - y = mx + c, where m is the gradient and c is the y intercept (value of y when x = 0)

Equation of the least squares regression line of y on x -

b = Sxy/Sxx and a = (mean of)y - b(mean of x)

y = a + bx

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## Interpolation/Extrapolation

Interpolation -

Using the least squares regression (on other side), to estimate the value of the dependent variable for a given value for the independant variable within the original range of values for the independant variable

Extrapolation -

Using least squares regression, to estimate the value of the dependant variable for a given value for the independant variable outside of the original range of values for the independant variable

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