Question

Total revenue of a company is steadily increasing since 2005. The following table displays sales (in millions of dollars) in the past few years.

Year Sales

2005 12

2007 19

2010 21

2012 25

2013 26

2015 30

(a) Compute the equation of the linear regression line.
(b) Display the data in a graph together with the linear regression line. (c) Compute r.
(d) Use the linear regression equation to estimate the revenue for 2019.

Answer 1

(a)

Following table shows the calculations:

	Year, X	Sales, Y	X^2	Y^2	XY
	2005	12	4020025	144	24060
	2007	19	4028049	361	38133
	2010	21	4040100	441	42210
	2012	25	4048144	625	50300
	2013	26	4052169	676	52338
	2015	30	4060225	900	60450
Total	12062	133	24248712	3147	267491

Sample size: n = 6

Now,

Slope of the regression equation is

and intercept of the equation will be

So the regression equation will be

y'= -3265.7616 +1.6355 *x

(b)

The coefficient of correlation is :

(d)

The required estimate for x = 2019 is

y'= -3265.7616 +1.6355 * 2019 = 36.3129