ACCA F5 - Performance Management
From Article "Forecasting technique Part2"
Correlation and Coefficient of correlation
Variables in two different datasets/groups/population, which
are not controlled by the experimenter may be related to each other. The
measure of relation between two variables is correlation. E.g. temperature and
the sales of ice-cream. Here, both the temperature and sales are not under the
control of experimenter and applying our common sense we know the rise in
temperature increases sales and the fall in temperature decreases sales. This
type of correlation is positive correlation.
Now, the question is how strongly the two variables are
correlated? Coefficient of correlation measures strength of relationship. Its
value range from +1.0 (perfect positive co-relation) to 0 (no correlation to -1
(perfect negative co-relation). The higher the value towards +1 the stronger
the positive relationship and…….
The approach for correlation calculation using Excel 2007 is
same as using regression. For the manual calculation, the following formula is
used for calculating correlation between two variables X and Y.
The simple correlation coefficient "r"
r = (n ∑xy - ∑x ∑y) / √ ( (n∑x2 - (∑x)2)
(n∑y2 - (∑y)2) )
Main disadvantage of correlation coefficients is that it
only measures linear relationship and coefficient only tells about the
relationship but not - what caused the relationship and how one variable effect
others.
Coefficient of determination (r2 ): Coefficient
of determination shows the variability of a factor caused or explained by its
relationship to another factor. Value is presented in percentage. High value
suggests high degree of linear-correlation of variables.
Correlation studies the performance relationship between two
members of a group/team/ project and as well to the spread of financial
contagion from one market to another. A simple correlation is a numerical
measure of linear relationship between two variables. A partial correlation measures
relation of one dependent variable and one independent variable form sets of
variables, assuming all other independent variables are constant. A multiple
correlation study the relation between sets of variables (i.e. the study of
three or more than three variables).
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