Answer to Question #217907 in Statistics and Probability for saad

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

$\hat {Y}=a+bX$

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

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

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

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

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