Question

The following table of values gives a company's annual profits in millions of dollars. Rescale the data so that the year 2001 corresponds to  x = 0.

Year	2001	2002	2003	2004	2005	2006
Profits (in millions of dollars)	23.8	25.2	26.3	28.9	27.6	28.4

Use the cubic regression model to predict the company's profits in 2010.

a) $14.5 million

b) $30.3 million

c) $32.8 million

d) $67.9 million

e) $6.8 million

f) None of the above

Answer 1

Rescale the data so that we get data as

Year	0	1	2	3	4	5
Profits (in millions of dollars)	23.8	25.2	26.3	28.9	27.6	28.4

so for the above data we get  the cubic regression model as

y=-0.0389 x^3+0.0667 x^2+1.5294 x+23.7238

to predict the company's profits in 2010

substitute x = 9

y =-0.0389 ( 9 )^3+0.0667 (9 )^2+1.5294 (9)+23.7238

= 14.533

y = 14.5

Answer : Option ( a )   $14.5 million