Question

The data for a certain test is provided below

X 100 200 300 400 500 600 700

Y 30 50 60 80 100 110 130

Compute the value of the correlation.

Find the equation of the regression lime.

Answer 1

 correlation:

$r=\frac{\sum (x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum (x_i-\overline{x})^2\sum(y_i-\overline{y})^2}}=0.9972$

regression line:

$y=ax+b$

$a=\frac{\sum (x_i-\overline{x})(y_i-\overline{y})}{\sum (x_i-\overline{x})^2}=0.1643$

$b=\overline{y}-a\overline{x}=14.2857$

$y=0.1643x+14.2857$