Can I get your help on some Maths and possibly Excel?

I have benchmarked my app increasing the number of iterations and number of obligors recording the time taken in seconds with the following result:

```
200 400 600 800 1000 1200 1400 1600 1800 2000
20000 15.627681 30.0968663 44.7592684 60.9037558 75.8267358 90.3718977 105.8749983 121.0030672 135.9191249 150.3331682
40000 31.7202111 62.3603882 97.2085204 128.8111731 156.2443206 186.6374271 218.324317 249.2699288 279.6008184 310.9970803
60000 47.0708635 92.4599437 138.874287 186.0576007 231.2181381 280.541207 322.9836878 371.3076757 413.4058622 459.6208335
80000 60.7346238 120.3216303 180.471169 241.668982 300.4283548 376.9639188 417.5231669 482.6288981 554.9740194 598.0394434
100000 76.7535915 150.7479245 227.5125656 304.3908046 382.5900043 451.6034296 526.0730786 609.0358776 679.0268121 779.6887277
120000 90.4174626 179.5511355 269.4099593 360.2934453 448.4387573 537.1406039 626.7325734 727.6132992 807.4767327 898.307638
```

How can I now come up with a function for T (time taken in seconds) as an expression of number of obligors O and number of iterations I

Thanks

I’m not quite sure of the data involved due to the question construction/presentation.

Assuming you’re looking for `y = f(x)`

. If you load the data into Excel, you can use the methods `SLOPE`

and `INTERCEPT`

on the data ranges to derive an expression of the form

```
y = mx+c
```

and thus a linear function.

If you want a quadratic or cubic, you can use `LINEST`

with a column of time data squared/cubed etc. to give you quadratic/cubic parameters, and thus derive an appropriate higher order function.

### Answer：

Spoke to one of the quants here the function is of the from T = KNO, where T is time, K some constant, N iterations, O obligors.

Rearrange for K = T/(NO), plug this into my sample data, take the average of all sample points, use the Std dev for the error

I did this for my data and get:

T = 3.81524E-06 * N * O (with 1.9% error), this is a pretty good approximation.

### Answer：

Create a chart in Excel, add a trendline, and select to have the equation displayed on the chart.

### Answer：

To clarify: You have tabular data below which you want to fit to some function f(O,I)=t?

```
200 400 600 800 1000 1200 1400 1600 1800 2000
20000 15.627681 30.0968663 44.7592684 60.9037558 75.8267358 90.3718977 105.8749983 121.0030672 135.9191249 150.3331682
40000 31.7202111 62.3603882 97.2085204 128.8111731 156.2443206 186.6374271 218.324317 249.2699288 279.6008184 310.9970803
60000 47.0708635 92.4599437 138.874287 186.0576007 231.2181381 280.541207 322.9836878 371.3076757 413.4058622 459.6208335
80000 60.7346238 120.3216303 180.471169 241.668982 300.4283548 376.9639188 417.5231669 482.6288981 554.9740194 598.0394434
100000 76.7535915 150.7479245 227.5125656 304.3908046 382.5900043 451.6034296 526.0730786 609.0358776 679.0268121 779.6887277
120000 90.4174626 179.5511355 269.4099593 360.2934453 448.4387573 537.1406039 626.7325734 727.6132992 807.4767327 898.307638
```

A rough guess looks like both O & I are linear. So f is in the form t = aO + bI + c. Plug in a few (O,I,t) and see what a,b,c should be.

Tags: excelexcel, time