$b_{yx} = \dfrac{400}{25} = 16$; then $\hat{y} = \bar{y} + b_{yx}(x-\bar{x}) = 500 + 16(40-30) = 660$ units.

GSEB Class-12 Statistics, Linear Regression (prediction):

We predict supply $y$ from price $x$, so use the regression line of $Y$ on $X$.

Regression coefficient of $Y$ on $X$:

$b_{yx} = \frac{\text{Cov}(x, y)}{S_x^2} = \frac{400}{25} = 16$

($S_x^2 =$ variance of $x = 25$.)

Regression line of $Y$ on $X$:

$\hat{y} = \bar{y} + b_{yx}(x - \bar{x})$

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