Fundamentals of Business Mathematics
Correlation analysis is a useful forecasting tool, but it’s important not to jump to the conclusion, if a strong correlation between a pair of factors is found, that variations in one are the result of variations in the other
Two variables are said to correlate if a change in one of them is accom panied by a predictable change in the other. The concept of correlation is commonly encountered in a range of techniques used in business forecasting and modelling.
This is a plausible finding, given that performance in exams is an expression of academic ability. An able student should score relatively highly in both exams, while a weak student should score lower marks in both.
An r score of 1 means that all of the points will again lie on a straight line when plotted on a graph, but this time the line has a negative gradient. We can still use this knowledge to make forecasts. If a student obtains 68 per cent in maths, we can predict that they will score 32 per cent in the English exam. This is an inherently implausible situation, but it serves to illustrate the point.
In this case the English marks average 0.666 of the maths marks, but there are small variations around that average in individual cases. Despite this, the degree of correlation may be considered high enough for forecasting purposes. If a student achieves a mark of 68 per cent in maths, say, we can predict that they will score 45 per cent in the English exam.
Nevertheless, correlation analysis remains a significant tool in business research. For example, one recent study was described by its authors as follows: “We develop a model using financial data for 311 publicly listed retail firms for the years 1987 to 2000 to investigate the correlation of inventory turnover with gross margin, capital intensity and sales surprise (the ratio of actual sales to expected sales for the year). The model explains 66.7 per cent of the withinfirm variation and 97.2 per cent of the total variation (across and within firms) in inventory turnover.”2