NDA Math Statistics Part 2

Concept: Co-efficient of Correlation (r): In simple linear regression analysis, the co-efficient of correlation is a statistic which indicates an association between the independent variable and the dependent variable. The co-efficient of correlationis represented by " $r$ " and its value lies between $-1.00$ and $+1.00$. - When the co-efficient of correlation is positive, such as $+0.80$, it means the dependent variable is increasing\/decreasing when the independent variable is increasing/decreasing. A negative value indicates an inverse association; the dependent variable is increasing/decreasing when the independent variable is decreasing\/increasing. - A co-efficient of correlation of $+0.8$ or $-0.8$ indicates a strong correlation between theindependent variable and the dependent variable. An $r$ of $+0.20$ or $-0.20$ indicates a weak correlation between the variables. When the co-efficient of correlation is $0.00$, there is no correlation. $r=\;\frac{ \Sigma (x_i - \overline{x})(y_i - \overline{y}) }{ \sqrt{ \sum (x_i - \overline{x})^2 \sum (y_i \overline{y})^2 } }$ Calculation: From the properties/nature of the co-efficient of correlation, we know that the correlation coefficient is independent of the choice of origin and scale.