how to find an asymptote from a scatter plot

[Ming]

Hi,

I'm trying to determine the speed that a runner reaches at the end of a 3min all out effort.  I have collected time and speed (at that given time) and when plotted on a scatter plot, it looks like it goes to an asymptote.  Is there a procedure in SAS that can determine that asymptote speed?  I wanted to use PROC NLIN but I don't know the function so I looked into PROC TRANSREG and the spline sometimes gives me the asymptote but sometimes it curves up at the end... Theoretically, it should be a smooth exponential decay or inverse curse from time zero to time (>3min).

here are my data...

time(s)	speed (m/s)
7.8	6.41
11.46	6.83
15.11	6.85
31.4	6.37
34.9	7.14
39	6.10
43.78	5.23
48.14	5.73
52.77	5.40
57.8	4.97
62.3	5.56
67.1	5.21
72.2	4.90
76.6	5.68
81.4	5.21
87.75	3.94
92.89	4.86
98.05	4.84
103.8	4.35
109.1	4.72
114.3	4.81
119.9	4.46
124.8	5.10
130.2	4.63
136.6	3.91
142	4.63
147.71	4.38
153.2	4.55
158.7	4.55
164.3	4.46
169.9	4.46
175.1	4.81
180.4	4.72

any help will be great!

thanks!

ming

[PGStats · Accepted solution]

Try

proc nlin data=test;
parms Vo=2.5 a=-0.017 Vf=4.5;
model speed = Vo*exp(a*seconds) + Vf;
output out=outTest predicted=predSpeed;
run;

proc sgplot data=outTest noautolegend;
series x=seconds y=predSpeed;
scatter x=seconds y=speed;
yaxis min=0;
run;

Initial speed is Vo + Vf. Asymptotic speed is Vf.

                                          Approx       Approximate 95% Confidence
            Parameter      Estimate    Std Error                 Limits

            Vo               3.1430       0.3154      2.4989      3.7870
            a               -0.0176      0.00493     -0.0277    -0.00751
            Vf               4.2795       0.2463      3.7765      4.7826

Seems to fit well...

PG

[Ming]

thanks for your help!

I tried it on another set of data with 4 data points, it didn't fit as well, but if I play around with the starting points for Vo, a, and Vf... sometimes I can get it to converge.

ming

[PGStats]

Fitting a 3-parameter curve on 4 points doesn't give much freedom!

Given times T1-T4 and speeds S1-S4, you can try :

Vo=S1-S4, Vf=S4, a=-1.4/(T2+T3)

as starting values.

Good luck!

PG