Reference no: EM13342757

The head of research and development (R&D) of a large chemical manufacturing company believes that the company's annual profits depend on the amount spent on R&D. The new chief executive officer disagrees and has asked for evidence. The head of R&D therefore wants an equation for predicting annual profits from the amount budgeted for R&D.

The following table presents relevant historical information for the preceding 6 years.

Let X = Amount Spent on R&D, and Y = Annual Profit (both in $ million):

Year X Y XY X^2

2006 2 20 40 4
2007 3 25 75 9
2008 5 34 170 25
2009 4 30 120 16
2010 11 40 440 121
2011 5 31 155 25

Totals 30 180 1,000 200

a) Use the least-squares method to derive the linear regression equation describing the relationship between R&D expenditure and annual profit.

b) Use the regression equation to predict annual profit in 2012 if the company budgets to spend $8 million for R&D that same year.

c) Would it be meaningful to use the regression equation to predict annual profit if the company decided to double R&D expenditure to $16 million in 2012? Explain reasoning.