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### Tool to best fit a two-term exponential?

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```Greetings good SAS people,

On July 16 ff. in "Use SAS to fit this curve?", I inquired as to what tool
I could use to find a best fit for some data.

In subsequent manual tinkering, I have found that this data (appended) is
very nicely fit by a two-term exponential equation such as:

Sites  =  773e^(-0.27*Chems)  +  156e^(-0.067*Chems)

(It is plotting the number of major U.S. hazardous waste sites at which
e.g. for Chems=1, 1 or more chemicals were in a pathway to which people
were exposed. Overall, the curve shows how often (the number of waste
sites) there is a high number of chemicals in the pathway, when folks are
exposed.)

The data itself makes a very "nice" curve to the naked eye, but a one-term
exponential simply wasn't cutting it. Two exp. terms were found to do a
lovely fit. However, this was all done "by hand" (in Excel, watching how
well my model fit vs. the data on a graph) and I have no tool to give me
feedback relative to R^2 values etc. (I guess I should bone up and can
probably do regression in Excel?... anybody have a quick webpage reference
handy?) Nor do I know whether/if SAS (or some other s/w) has the ability to
make and/or fit a two term exponential. I played around with Insight as a
result of the previous post, but it has so many arcanes variables (a.k.a.
I'm such a newbie) I can't tell whether it can try to fit with a two term
exponential. (I'm not interested in polynomial fits, and that's the only
thing I was able to figure out how to get Insight to work.)

Thanks in advance if you can help!!

Mike, Atlanta

***

input Chems Sites;

cards;

1 743
2 588
3 475
4 390
5 321
6 266
7 214
8 185
9 161
10 136
11 111
12 102
13 87
14 74
15 69
16 61
17 56
18 52
19 47
20 46
21 44
22 39
23 36
24 33
25 29
26 26
28 24
29 22
30 20
31 19
32 18
37 16
38 15
39 13
40 11
41 10
42 9
48 7
49 6
51 5
56 4
58 3
62 2

;
```
 0
Reply rmf4 (6) 8/1/2003 3:04:00 PM

```PROC CAPABILITY, part of the SAS/QC package, has some very nice tools for
curve-fitting. Part of PROC CAPABILITY's histogram functionality was added
to PROC UNIVARIATE in Base SAS, but not the curve-fitting features. You do
have to tell it what distribution to attempt to fit.

Jonathan Siegel

On Fri, 1 Aug 2003 11:04:00 -0400, Mike Fay <rmf4@CDC.GOV> wrote:

>Greetings good SAS people,
>
>On July 16 ff. in "Use SAS to fit this curve?", I inquired as to what tool
>I could use to find a best fit for some data.
>
>In subsequent manual tinkering, I have found that this data (appended) is
>very nicely fit by a two-term exponential equation such as:
>
>   Sites  =  773e^(-0.27*Chems)  +  156e^(-0.067*Chems)
>
>(It is plotting the number of major U.S. hazardous waste sites at which
>e.g. for Chems=1, 1 or more chemicals were in a pathway to which people
>were exposed. Overall, the curve shows how often (the number of waste
>sites) there is a high number of chemicals in the pathway, when folks are
>exposed.)
>
>The data itself makes a very "nice" curve to the naked eye, but a one-term
>exponential simply wasn't cutting it. Two exp. terms were found to do a
>lovely fit. However, this was all done "by hand" (in Excel, watching how
>well my model fit vs. the data on a graph) and I have no tool to give me
>feedback relative to R^2 values etc. (I guess I should bone up and can
>probably do regression in Excel?... anybody have a quick webpage reference
>handy?) Nor do I know whether/if SAS (or some other s/w) has the ability to
>make and/or fit a two term exponential. I played around with Insight as a
>result of the previous post, but it has so many arcanes variables (a.k.a.
>I'm such a newbie) I can't tell whether it can try to fit with a two term
>exponential. (I'm not interested in polynomial fits, and that's the only
>thing I was able to figure out how to get Insight to work.)
>
>Thanks in advance if you can help!!
>
>   Mike, Atlanta
>
>***
>
>input Chems Sites;
>
>cards;
>
> 1 743
> 2 588
> 3 475
> 4 390
> 5 321
> 6 266
> 7 214
> 8 185
> 9 161
> 10 136
> 11 111
> 12 102
> 13 87
> 14 74
> 15 69
> 16 61
> 17 56
> 18 52
> 19 47
> 20 46
> 21 44
> 22 39
> 23 36
> 24 33
> 25 29
> 26 26
> 28 24
> 29 22
> 30 20
> 31 19
> 32 18
> 37 16
> 38 15
> 39 13
> 40 11
> 41 10
> 42 9
> 48 7
> 49 6
> 51 5
> 56 4
> 58 3
> 62 2
>
>;
```
 0
Reply jmsiegel (9) 8/4/2003 11:22:11 PM

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