--SIMPLE LINEAR REGRESSION--

SIMPLE LINEAR REGRESSION is used to MODEL THE RELATIONSHIP BETWEEN TWO VARIABLES. The aim is to predict the value of a DEPENDANT VARIABLE (e.g., sales) based on changes in the value of an INDEPENDANT VARIABLE (e.g., number of selling staff or the price level).

CORRELATION means using statistical analysis to MEASURE THE STRENGTH OF TH ERELATIONSHIP BETWEEN TWO VARIABLES. Correlation can be measured in a number of different ways and the most widely used method is PEARSON'S CORRELATION COEFFICIENT.

The results of the correlation coefficient are ALWAYS BETWEEN −1 AND 1. However, the correlation result DOES NOT TELL US WHY? and HOW? the relationship exists; it just suggests that the relationship exists.

A CORRELATION COEFFICIENT OF 1 means that for every POSITIVE INCREASE in one variable, there is a POSITIVE INCREASE of a fixed proportion in the other. In business terms this result is unlikely. For example, the relationship between airline ticket prices and the price of oil will be very high, but other airline cost factors mean that the correlation between the two will never equal 1. 

A CORRELATION COEFFICIENT OF -1 means that for every POSITIVE INCREASE in one variable, there is a NEGATIVE DECREASE of a fixed proportion in the other. Again, in business this result is unlikely, but a logistics business will understand that the amount of fuel remaining in a  delivery truck’s tank will reduce in negative correlation to its average speed. 

A CORRELATION COEFFICIENT OF ZERO means that for every INCREASE in the independent variable, there is NOT A POSITIVE OR A NEGATIVE CHANGE in the dependent variable. The two variables are just NOT RELATED. 

EXTRAPOLATION (Meaning to 'extend') involves making statistical forecasts by using historical trends that are projected for a specified period of time into the future. It is only used for time-series forecasts – where, for example, sales data has been gathered over a period of time. 

The simplest method of extrapolation is to extend the line of best fit (based on a scatter diagram) into future time periods. This line can then be used to read off forecasts for sales in future – although to be more accurate, these forecasted figures should be adjusted for regular seasonal and cyclical fluctuations.