Projection (y) = a + bx

Equation I To calculate Projected rainfall/temperature

$Slope=\overline{y}-\overline{b}x$

Equation II To calculate Slope (b) of regression line

$Y=r\frac{S_y}{S_x}$

Equation III To calculate Y-Intercept (a) of regression line Intercept

$r=\frac{{{\displaystyle \sum }}^{\text{}}\left(\left(x-\overline{x}\right)\left(y-\overline{y}\right)\right)}{\sqrt{{{\displaystyle \sum }}^{\text{}}{\left(x-\overline{x}\right)}^2{{\displaystyle \sum }}^{\text{}}{\left(y-\overline{y}\right)}^2}}$

Equation IV To calculate Correlation Coefficient (Pearson’s r)

$S_y=\sqrt{\frac{{{\displaystyle \sum }}^{\text{}}{\left(y-\overline{y}\right)}^2}{n-1}}$

Equation V To calculate Standard Deviation of y (S_y)

$S_x=\sqrt{\frac{{{\displaystyle \sum }}^{\text{}}{\left(x-\overline{x}\right)}^2}{n-1}}$

Equation VI To calculate Standard Deviation of x (S_x)