Question

find the most likely price in mumbai corresponding to the price of RS 70 of Kolkata from the following arrange price Kolkata 65 mumbai 67 standard deviation kolkata 2.5 mumbai 3.5 correlation coefficient between the price of commodities in the two cities​

Answer 1

Given:

According to question we have

$\overline{\mathrm{x}}=65 \\\overline{\mathrm{y}}=67\\\sigma_{\mathrm{x}}=2.5,\\\sigma_{\mathrm{y}}=3.5\\\rho=0.8$

$\text { regression line of } y \text { on } x \text { is }$

$\begin{array}{l}\mathrm{y}-\overline{\mathrm{y}}=\rho \frac{\sigma_{\mathrm{y}}}{\sigma_{\mathrm{x}}}(\mathrm{x}-\overline{\mathrm{x}}) \\\end{array}$

$\mathrm{y}-67=\frac{0.5 \times 3.5}{2.5}(\mathrm{x}-65)$

$\mathrm{y}-67=\frac{1.75}{2.5}(\mathrm{x}-65)$

$\mathrm{y}-67=\frac{175}{25}(\mathrm{x}-65)$

$\text { putting } x=70$

$y-67=\frac{175}{25}(70-65)$

$y-67=\frac{175}{25}(5)$

$y-67=\frac{175}{5}$

y - 67 =35

y = 35 + 67

y = Rs.102

Hence the required value is Rs.102