In this case some of the points are on the line and some are above and below, but most are close to the line which suggests that there is a relationship between activity level and the total production cost.

This ‘line of best fit’ can be used to predict what will happen at other levels of production. For levels of production which don’t fall within the range of the previous levels, it is possible to extrapolate the ‘line of best fit’ to forecast other levels by reading the value from the chart.

This is a straightforward technique, but it has some limitations. The main one being that the ‘line of best fit’ is estimated from the data points plotted and different lines may be drawn from the same set of data points. A method which can overcome this weakness is regression analysis.

#### Regression analysis

Regression analysis also uses the historic data and finds a line of best fit, but does so statistically, making the resulting line more reliable.

We assume a linear (straight line) relationship between the variables and that the equation of a straight line is:

**y = a + bx**

where:

a is the fixed element (where the line crosses the y axis)

b is the variable element (gradient of the line) and

x and y relate to the x and y variables.

a and b are calculated using the following formulae: