Question

Given the following set of values,

Corn Yield (Y) 10, 15, 30, 35, 25, 30, 50, 45

Fertilizer (X) 0.3, 0.6, 0.9, 1.2, 1.5, 1.8, 2.1, 2.4

Determine the equation of least square regression line.

Answer 1

$\hat {Y}=a+bX$

$b = \frac{\sum_{i=1}^{n} (x_i-\bar{x})(y_i-\bar{y})}{\sum_{i=1}^{n} (x_i-\bar{x})^2}$

$a = \bar{y} - b\bar{x}$

$b=\frac{61.5}{3.78}=16.27$

$a=30-(1.35\times16.27)=8.036$

$\hat {Y}=8.036+16.27X$