Page 57 - BA2 Integrated Workbook STUDENT 2018

Analysing and predicting costs

5.2 Correlation coefficient

Pearson’s correlation coefficient measures the amount of linear correlation
present in a set of pairs of data. It is denoted as r.

r always lies in the range –1 to +1, where:

r = +1 denotes perfect positive linear correlation

r = –1 denotes perfect negative linear correlation

r = 0 denotes no linear correlation

5.3 Coefficient of determination

Pearson's correlation coefficient allows us to discuss the strength of the relationship
between two sets of figures. However, the interpretation of the figure is made slightly
easier if we square the correlation coefficient, r, to give the coefficient of
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determination, r .
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The coefficient of determination, r , gives the proportion of changes in y that can be
explained by changes in x, assuming a linear relationship between x and y.

For example:

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If a correlation coefficient r = +0.9, then r = 0.81 and we could state that 81% of the
observed changes in y can be explained by the changes in x and that 19% of the
changes must be due to other factors.

Illustrations and further practice

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