Please! Please help me with this math problem! What does the last part mean?

Question

Pleeeeease help me out. I put this in the graphing calculator

Year: 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993

R: 11.09, 13.27, 14.45, 15.97, 17.58, 18.61, 19.08, 19.39

This is the formula the calculator gave me after going to STATS & CALC:

y=ax+b

a=1.2052380952

b=-2381.64119

r=.97641394892

So I thought the answer was R=1.21t-2381.6. But the book says the answer is R=1.21t+4.73. Why is the last part different?

What does the book mean when it says, "Let t represent the year, with t=6 corresponding to 1986?" Is this why our answers are different?

Answer 1

The book expected you to put the year 1986 as just 6.  You put it in as 1986.

Lets look at this closely, because you did a nice job of bringing up a point in regressions.

the line is in the form y = ax + b, or in this case r = at + b.  The slope of the line is a, or 1.21.  It agrees because in both the book case (using year 6, 7, 8, 9) and your method ( 1986, 1987....) the value goes up 1.21 for each year.

Now, the bias (the b term) is different. The bias is also the Y intercept.  You started with high year numbers, so that 1.21t will generate a very large number.  You need to subtract a large number (which is surprisingly close to 1.21*1978) in order to bring the line down to the right level.  The book used lower numbers (years were 6, 7,8,9,10), so it had to raise the line higher to meet the numbers.  

Ok, here is the kicker.  If you recoded the years just right, your bias would be zero, and the formula would be R = 1.21t.    I haven't figured out what those recoded years would be but I'll bet it would be the actual year minus about 1978.  

I hope I haven't confused you too much here.  

Answer 2

Instead of 1986, 1987, etc use 6, 7, etc as required by the book and you'll get the same answer.