Subject: Applied Mathematics 4

Topic: Correlation & Regression

Difficulty: Medium

$\bar{x} = 5 \\ \bar{y} = 10 $

$ 20y = 9x + 40 \\ y = \frac{9}{20}x + \frac{40}{20} \\ \therefore y = \frac{9}{20}x + 2 \\ b_{yx} = \frac{9}{20} $

Equation of lines of regression of 'y' on 'x' is given by:

$ (y - \bar{y}) = b_{yx}(x - \bar{x}) \\ (y - 10 ) = \frac{9}{20}(x - 5) \\ y - 10 = \frac{9}{20}x - \frac{45}{20} \\ y = \frac{9}{20}x - \frac{9}{4} + 10 \\ \therefore y = \frac{9}{20}x + \frac{31}{4} $

When x = 30

$ y = \frac{9}{20}(30) + \frac{31}{4} \\ y = \frac{27}{2} + \frac{31}{4} \\ \therefore y = \frac{85}{4} = 21.25 $