A) Find the correlation coefficient between X and Y. X = [45, 50, 56, 62, 65, 70], Y = [65, 70, 75, 80, 90, 100]

$X = [45, 50, 56, 62, 65, 70]$
$Y = [65, 70, 75, 80, 90, 100]$
The number of data points is $n=6$.

• $\sum X = 45+50+56+62+65+70 = 348$
• $\sum Y = 65+70+75+80+90+100 = 480$
• $\sum XY = (45 \times 65) + (50 \times 70) + (56 \times 75) + (62 \times 80) + (65 \times 90) + (70 \times 100)$ $\sum XY = 2925 + 3500 + 4200 + 4960 + 5850 + 7000 = 28435$
• $\sum X^2 = 45^2 + 50^2 + 56^2 + 62^2 + 65^2 + 70^2$ $\sum X^2 = 2025 + 2500 + 3136 + 3844 + 4225 + 4900 = 20630$
• $\sum Y^2 = 65^2 + 70^2 + 75^2 + 80^2 + 90^2 + 100^2$ $\sum Y^2 = 4225 + 4900 + 5625 + 6400 + 8100 + 10000 = 39250$

The formula is:

Substitute the calculated values:

The correlation coefficient between X and Y is $\boxed{0.9664}$.

First, calculate the slope $b$:

Using values from part (a):

Next, calculate the means $\bar{X}$ and $\bar{Y}$:

Now, calculate the y-intercept $a$:

The regression equation of X on Y is $X = 2 + 0.7Y$.

Substitute $Y = 150$ into the regression equation:

The supply when the price of the commodity is Rs. 150 is $\boxed{107}$.