## Regression

In GCSE you draw a

Regression enables this line to be

**line of best fit**.Regression enables this line to be

**mathematically worked out**## Line of Best Fit

For a regression line of bivariate data the equation is

**y = a + bx**(same thing as y = mx + c except values are switched)**b**is the gradient**b =**__Sxy__**Sxx****a**is the y intercept## Coding

In coding the

In an exam you may be asked to find the regression line equation for the coded data

E.g.

If you've discovered the regression line is

and the coding was

Giving

use algebra to discover the coded line is

**regression line may not be the same**.In an exam you may be asked to find the regression line equation for the coded data

E.g.

If you've discovered the regression line is

**y = 36 - 5x**and the coding was

**x = 10c**and**y = 2 + m****Substitute**these values inGiving

**2 + m = 36 - 5(10c)**use algebra to discover the coded line is

**m = 34 - 50c**## Interpolation and Extrapolation

**Interpolation**- estimate value within data range

**Extrapolation**- estimate value out of data range

You do this by

**using the regression line**and substituting in x and y values

The

**more you extrapolate**the

**less reliable the result**is as the data may follow a different trend out of the range collected