Question

Calculate coefficient of correlation with the help of following data by using step deviation method.

$\begin{array}{cccccc}PriceIndex& 120& 150& 190& 220& 230\\ MoneySupply(Rs.incrore)& 1800& 2000& 2500& 2700& 3000\end{array}$

Answer 1

Let X and Y denote price index and money supply, respectively.
Calculation of coefficient of correlation:

$\begin{array}{ccccccccc}X& dx=(X-A)& C_1=10& d{x}^{\prime 2}& Y& dy=(Y-A)& C_2=10,& d{y}^{\prime 2}& d{x}^{\prime }d{y}^{\prime }\\ & A=190& d{x}^{\prime }=\frac{dx}{C_1}& & & A=2500& d{y}^{\prime }=\frac{dy}{C_2}& & \\ 120& -70& -7& 49& 1800& -700& -7& 49& 49\\ 150& -40& -4& 16& 2000& -500& -5& 25& 20\\ 190& 0& 0& 0& 2500& 0& 0& 0& 0\\ 220& 30& 3& 9& 2700& +200& +2& 4& 6\\ 230& 40& 4& 16& 3000& +500& +5& 25& 20\end{array}$

Here, N=5, $\sum d{x}^{\prime }=-4,\sum d{x}^{\prime 2}=90,\sum d{y}^{\prime }=-5,\sum d{y}^{\prime 2}=103$ and $\sum d{x}^{\prime }d{y}^{\prime }=95$
$r=\frac{\sum d{x}^{\prime }d{y}^{\prime }-\frac{\sum d{x}^{\prime }\times \sum d{y}^{\prime }}{N}}{\sqrt{\sum d{x}^{\prime 2}-\frac{(\sum d{x}^{\prime }{)}^2}{N}}\times \sqrt{\sum d{y}^{\prime 2}-\frac{(\sum d{y}^{\prime }{)}^2}{N}}}$
$=\frac{95-\frac{-4\times -5}{5}}{\sqrt{90-\frac{(-4{)}^2}{5}}\sqrt{103-\frac{(-5{)}^2}{5}}}=\frac{95-4}{\sqrt{90-3.2}\sqrt{103-5}}$
$=\frac{91}{\sqrt{86.8}\times \sqrt{98}}=\frac{91}{9.32\times 9.92}=\frac{91}{92.268}=0.99$

It shows that there is a strong positive correlation between price index and money supply.