Find relation / formula between series and a number

Hi,

I need to get the relation of 2 numbers with 2 series: „Series 1“ was obtained, using a certain parameter = 0.7 And „Series 2“ was obtained, only by changing the same parameter to 0.4

I need to obtain the formula (relation) between each number and the series.

My goal is to have a series with this parameter = 0.0 and use this „formula/relation“ to get the values of the series, when the parameter is = 0.1, 0.2, 0.3, 0.4 …..

P.S. – How did I came up with this series?

The data is taken from „lifetime/fatigue“ testing of shafts. It shows how much load can the shaft withstand for certain numbers of cycles. The parameter changed is the depth of a hardening of the surface. The numbers in one series were taken from a trend-line for „easy to calculate“ numbers e.g 1000, 2000, 5000 – not 5467 I don’t really care if MATLAB or EXCEL is used, as long as it does the job…

Series 1 - for 0.7

924.8114
928.6449
932.7028
937.0121
941.6044
946.518
951.7991
957.5045
963.7052
970.4914
977.9796
986.3247
995.7381
1006.519
1019.109
1034.204
1052.984
1077.699
1113.521
1177.538
1187.586
1198.92
1211.901
1227.061
1245.236
1267.847
1297.605
1340.737
1417.817

and Series 2 - for 0.4

882.805
886.5866
890.5902
894.8424
899.3746
904.2247
909.4384
915.0722
921.1963
927.9001
935.2994
943.5475
952.8542
963.5164
975.9735
990.9151
1009.514
1034.008
1069.543
1133.141
1143.134
1154.409
1167.327
1182.419
1200.521
1223.054
1252.729
1295.781
1372.832

Thanks!

[Walter Roberson]

Your data has a sharp turn at the 20th data point. Unless both have significant measurement error, the curves cannot be polynomial or exponential or anything else that has a continuous first derivative. The two are also not linear in each other.

Testing, I can see that the curves are not piecewise polynomial.

Answer 1

[Roger Stafford]

Since the two series are approximately linearly related, I would suggest that it is simplest if the parameter also be considered linear. Let series 1 be called x and series 2 be called y. Let the parameter in question be called t. Then define a series z corresponding to parameter t as:

 z = ((.7-t)/.3)*x + ((t-.4)/.3)*y;

If t = .7, this gives just x. If t = .4, it is y. For t = .1, .2, .3, etc. it will presumably give you the respective series you seek. For any two values of t, the two respective series will also be linearly related.