Definition: A line of best fit is a straight line drawn through a scatter plot that follows the trend of the data, used to describe the relationship and make predictions.
What is a line of best fit?
It is a line that passes as close as possible to the points, with roughly as many above as below. It models a linear trend.
How do you draw one?
Look at the overall trend and draw a line that balances the points. It need not touch any of them. Then pick two points on the line, not necessarily data points, to find its equation.
What does an example show?
Suppose the line passes through (2, 30) and (8, 66). The slope is 36 / 6 = 6. Then 30 = 6(2) + b gives b = 18, so y = 6x + 18.
How do you interpret it?
The slope means a change of 6 units in y for each increase of 1 in x. The intercept 18 is the predicted y when x is 0, if that makes sense in context.
How do you predict?
For x = 5, y = 6(5) + 18 = 48. This is interpolation, within the data range. Predicting far outside the range is risky.
What is a common mistake?
Connecting the first and last points. The line must follow all the data.