Math Forum / Math Software / SAS / August 2003

On 19 Aug 03 14:38:24 GMT, Jianying.Zhang@UMASSMED.EDU (Zhang,
Jianying) wrote:

If you plot the 3 point you have, you'll see that a linear model
provides very poor fit. A good linear model would be one in which the
slope of the line joining consecutive points (ratio of change in x to
change in y) was fairly constant. In your case these values are
(2-1)/(.45-.37)=12.5, and (3-2)/(.46-.45)=100. Without further
information I don't think you should have any confidence in the
quality of a linear (or any other model) to predict the value in year
4.

JW

Jianying,

A mathematician would say:

  For any two points (x1,y1) and (x2,y2) with x1 ^= x2, then
  for any third value x, (x,y) is point on the line passing
  through the given points if and only if

      y1-y2     y - y2
      -----  =  ------
      x1-x2     x - x2

A statistician would say that your sample isn't large enough.

A physicist would say if x1=x2 then rotate the axes and go to the
mathematician and rotate his answer.

An engineer would say for year 4 the value is .467803

A Republican politician would say this shows we need more money for
military budget and a bigger tax cut.

A Democratic politician would say George W made the data.

So you see, we will have to know your occupation before a definitive
answer can be made.  Are you an economist by any chance?

IanWhitlock@westat.com
-----Original Message-----
From: Zhang, Jianying [mailto:Jianying.Zhang@UMASSMED.EDU]
Sent: Tuesday, August 19, 2003 10:38 AM
To: SAS-L@LISTSERV.UGA.EDU
Subject: a simple linear extrapolation

Hi, Dear SAS_L:

I have completely forgotten how to do a simple linear extrapolation.

I have three data points and would like to predict the fourth.

Year 1  .37
Year 2  .45
Year 3      .46

Do I average the change difference between Year1-Year2 and Year2-Year3???
And then add the avg change onto the Year 3 value???

Thanks in advance

Jianying Zhang

There's no such thing as a 'simple linear extrapolation'.

If you were to actually do this sort of extrapolation using
statistical software, you would find that your confidence bound
for your prediction interval would be so large that your point
estimate would be useless.  Especially when your three points
don't come close to lying on a straight line.  And you have time
data, with no effort to incorporate any time-series information
in your point estimate.

I strongly advise you not to put any value on any number picked
as the extrapolation from these data.

HTH,
David
--
David Cassell, CSC
Cassell.David@epa.gov
Senior computing specialist
mathematical statistician