CAT / FIA FMA Syllabus B. Data Analysis And Statistical Techniques - Scatter diagrams and lines of best fit - Notes ^{4 / 14}

Information about two related variables can be shown on a ‘scatter diagram’:

Y Axis

The Dependent variable

X Axis

The Independent variable

Y Axis (Dependent Variable)

In the chart below you can see:

• Sales is DEPENDENT on advertising

• Total Cost is DEPENDENT on how many units made

The Line of Best Fit

The "best-fit" line (trend line) is a straight line which passes as near to as many of the plots on the graph as possible. 

The further away (more scattered) the plots are away from the line means the less dependent they seem to each other and so the line of best fit is less reliable 

For example, if the plots look like this:

The line of best fit would be drawn as follows

and because the plots are very close to the line - it appears that Y is closely related to X (dependent upon)

Scatter Diagrams as a Forecasting Technique

We can use the line of best fit (the trend) to read off values for at any points on the axes...

1. We could extend the line of best fit (the trend) into the future - this is known as extrapolating the trend

2. Forecasting this way is relatively simple

3. Remember though it is only really a good technique if the plots are not scattered too far away from the line (trend)

Disadvantages of Using as a Forecasting Technique

• Uses past information to predict the future

• Assumes the relationship is linear

• Uses a line of best fit which is matched to the points on the scatter diagram by eye - this is likely to be a major cause on inaccuracy unless the points in the scatter are very tightly clustered together.

A more mathematical technique, regression analysis, is available to improve the accuracy of the line of best fit.