Problem:
It is 2007 and you are a newly minted MBA. Your employer sends you on a reconnaissance mission to Roswell, New Mexico. Your CEO wants to relocate the firm’s customer service operation to Roswell, but she is at odds with Dilbert, the recently appointed Director of Human Resources department. Dilbert says that the residents of Roswell have had a freakishly high rate of brain tumors, and insists that the rate will rise in the near future, making a relocation to Roswell an expensive mistake (as a result of higher-than-average health care bills for the firm’s Roswell employees). Dilbert attributes the high rate of brain tumors in Roswell to the 1997 crash of a mysterious flying vehicle carrying a cargo of kranium. Adhering to company policy, you don’t ask, and he doesn’t tell, whether he believes in UFOs.
Your assignment is to confirm or disconfirm Dilbert’s forecast of high health care bills in the near future. From your friends at Google.com, you find out that (1) kranium is a radioactive substance with a half-life of one year (meaning that each year, the radiation it emits is halved), and (2) it does indeed cause brain tumors, with the risk of brain tumors moving in line with the level of kranium radiation being emitted. From the Roswell hospital, you obtain the following data on the annual number of residents diagnosed with brain tumors during the 1997-2006 period:
YEAR TUMORS
1997 1039
1998 474
1999 275
2000 149
2001 92
2002 77
2003 4
2004 15
2005 22
2006 2
Using the hospital’s data, you estimate the following model:
ln (TUMORS) = 7.5 – 0.627 YEAR Adj-R2 = 0.86
t = 13.6 t = -7.1
where TUMORS = Number of brain tumor diagnoses in a given year
YEAR = 1 (for 1997) to 10 (for 2006)
Using a brand new Etch-a-Sketch, Dilbert estimates the following model, using the very same data:
TUMORS = 1174 - 328.7 YEAR + 22.0 YEAR2 Adj-R2=0.89
t = 9.1 t = -6.1 t = 4.6
How many tumors does your model predict for the year 2007? __________
How many tumors does Dilbert’s model predict for 2007? __________
Does your model support Dilbert’s opposition to the CEO’s plan?__________
Does Dilbert’s model support Dilbert’s opposition to the CEO’s plan?_________