Find the line of best fit of the following data using regres

Find the line of best fit of the following data using regression

1996 2570.5 19972734.5 19982897.5 1999 20003052.5 20013170.5 2002 2003 20044174.5 2005 2006 4648.5 2007 20085436.5 20095988.5 20106470.5 20116790.5 2012 2013 7027.5 20147196.5 2015 7086.5 3079 8 3528 3907 4250 4925 6871

Solution

A line of best fit is a straight line that is the best approximation of the given set of data. .

Let y = a + bx be the straight line which is fitted to the given data points

Then the normal equations are

y_i = na + b x_i

x_i y_i = ax_i + b x_i²

So that we need to find x_{i ,} y_{i ,} x_i y_i and x_i²

From the fiven data x_i = 40,110 , y_i =  95652 , x_i y_i = 179190915 and x_i² = 80441270 and n = 20

Substitute these values in the above normal equations, we get

95652 = 20a + 40110b

179190915 = 40110a + 80441270b

by solving these two equations we get

a = 578523909.521 and b = 288466.278195

Therefore, the best fit curve to the given data is

y = 578523909.521 + ( 288466.278195 ) x