Data, Statistics & Regression

Regression lines

Plotting approximate best fit line

Best fit lines can also be drawn approximately by eye. We start by finding the average x and y, giving the point (xˉ,yˉ). We then take a rule and place it on this point, and adjust the slope until we find a reasonable best fit line.

Regression line y on x

Linear regression is a statistical method used to model the relationship between two variables when data is given as pairs of points (x,y). We fit a straight line (called the regression line) that minimizes the average vertical distance from the points:

The general equation of the regression line is:

y=ax+b

where a is the slope and b is the y-intercept.

The values of a and b can be found using a calculator.

Example

x	3	4	5	6
y	8	12	16	17

Using a calculator, we find a=3.1 and b=−0.7. So the regression line is y=3.1x−0.7.

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