CBSE BoardEnglish MediumSTD 11 CommerceEconomicsCorrelation3 Marks
Question
What is Karl Pearson's coefficient of correlation? State its properties.
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Answer
Karl Pearson's coefficient of correlation, denoted by rk, measures the degree and direction of relationship between two variables. It is calculated as :$\text{r}_\text{k}=\frac{\Sigma\text{xy}}{\text{N}.\sigma_\text{x}.\sigma_\text{y}} \ \text{or}\ \frac{\Sigma\text{xy}}{\sqrt{\Sigma\text{x}^2}\sqrt{\Sigma\text{y}^2}}$
$\text{r}_\text{k}=\frac{\Sigma(\text{X}-\overline{\text{X}})(\text{Y}-\overline{\text{Y}})}{\sqrt{\Sigma(\text{X}-\overline{\text{X}})^2}\sqrt{\Sigma(\text{Y}-\overline{\text{Y}})^2}}$
$\text{where, x}=\text{X}-\overline{\text{X}},\text{y}=\text{Y}-\overline{\text{Y}}$ Properties of Karl Pearson's coefficient of correlation:
The value of correlation coefficient lies between -1 and +1. Symbolically, -1
Correlation coefficient is independent of the change of origin and scale, i.e., the value of ‘r, 'is unaffected by the change of origin and scale.
If r = 0, the two variables are not related. There is no linear relationship between them. They are independent.
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