Calculation of area under curve

General
1

Dear all,
May I have a simple question.
I would like to calculate the areas (B1 and B2) as in the following picture.
May I get your assistance how to code for that.
image

2

is there any mathematical description of the line separating the two areas ?

3

Dear @nirgrahamuk ,
I have a line graph using the data. I didn’t make a mathematical expression for that line.

4

Can you share the data or an example of similar data ?

5

The simplest way is to use trapz from the pracma package to use the trapezoidal method for numerical integration. You can simply supply vectors or x and y variables.

From your picture, B2 would be the integral of the function shown in the solid black line, and B1 would be the integral of the function shown by the dotted line (a straight line?) minus B2.

6
wlPGP time Rg30
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381.24 2015-01-08 12:30:00 UTC 0.033296022
381.24 2015-01-08 13:00:00 UTC 0.02684567
381.24 2015-01-08 13:30:00 UTC 0.040409047
381.24 2015-01-08 14:00:00 UTC 0.044119116
381.66 2015-01-08 10:30:00 UTC 0.02503945
381.66 2015-01-08 12:30:00 UTC 0.035039555
381.66 2015-01-08 13:00:00 UTC 0.02868045
381.66 2015-01-08 13:30:00 UTC 0.042423364
381.66 2015-01-08 14:00:00 UTC 0.046178574
382.09 2015-01-08 10:30:00 UTC 0.025987651
382.09 2015-01-08 12:30:00 UTC 0.036866352
382.09 2015-01-08 13:00:00 UTC 0.03010445
382.09 2015-01-08 13:30:00 UTC 0.044299989
382.09 2015-01-08 14:00:00 UTC 0.047176279
382.51 2015-01-08 10:30:00 UTC 0.02641904
382.51 2015-01-08 12:30:00 UTC 0.037534537
382.51 2015-01-08 13:00:00 UTC 0.033574302
382.51 2015-01-08 13:30:00 UTC 0.045364146
382.51 2015-01-08 14:00:00 UTC 0.04882672
382.93 2015-01-08 10:30:00 UTC 0.027409191
382.93 2015-01-08 12:30:00 UTC 0.03991552
382.93 2015-01-08 13:00:00 UTC 0.032073436
382.93 2015-01-08 13:30:00 UTC 0.048250145
382.93 2015-01-08 14:00:00 UTC 0.051710408
383.36 2015-01-08 10:30:00 UTC 0.026713694
383.36 2015-01-08 12:30:00 UTC 0.041464502
383.36 2015-01-08 13:00:00 UTC 0.034924916
383.36 2015-01-08 13:30:00 UTC 0.049052691
383.36 2015-01-08 14:00:00 UTC 0.051910146
383.78 2015-01-08 10:30:00 UTC 0.026765403
383.78 2015-01-08 12:30:00 UTC 0.041811226
383.78 2015-01-08 13:00:00 UTC 0.035574992
383.78 2015-01-08 13:30:00 UTC 0.051026774
383.78 2015-01-08 14:00:00 UTC 0.053182393
384.21 2015-01-08 10:30:00 UTC 0.026550824
384.21 2015-01-08 12:30:00 UTC 0.042337494
384.21 2015-01-08 13:00:00 UTC 0.033159187
384.21 2015-01-08 13:30:00 UTC 0.05073189
384.21 2015-01-08 14:00:00 UTC 0.052495704
384.63 2015-01-08 10:30:00 UTC 0.026234395
384.63 2015-01-08 12:30:00 UTC 0.03949219
384.63 2015-01-08 13:00:00 UTC 0.032134884
384.63 2015-01-08 13:30:00 UTC 0.048303615
384.63 2015-01-08 14:00:00 UTC 0.051682347
385.05 2015-01-08 10:30:00 UTC 0.026990194
385.05 2015-01-08 12:30:00 UTC 0.039202632
385.05 2015-01-08 13:00:00 UTC 0.031205505
385.05 2015-01-08 13:30:00 UTC 0.046572246
385.05 2015-01-08 14:00:00 UTC 0.049629099
385.48 2015-01-08 10:30:00 UTC 0.026544968
385.48 2015-01-08 12:30:00 UTC 0.038158555
385.48 2015-01-08 13:00:00 UTC 0.029480494
385.48 2015-01-08 13:30:00 UTC 0.044724409
385.48 2015-01-08 14:00:00 UTC 0.048300511
385.9 2015-01-08 10:30:00 UTC 0.026535107
385.9 2015-01-08 12:30:00 UTC 0.037899709
385.9 2015-01-08 13:00:00 UTC 0.029548011
385.9 2015-01-08 13:30:00 UTC 0.044619038
385.9 2015-01-08 14:00:00 UTC 0.047894545
386.32 2015-01-08 10:30:00 UTC 0.025665208
386.32 2015-01-08 12:30:00 UTC 0.036897979
386.32 2015-01-08 13:00:00 UTC 0.028757184
386.32 2015-01-08 13:30:00 UTC 0.04369846
386.32 2015-01-08 14:00:00 UTC 0.047168454
386.75 2015-01-08 10:30:00 UTC 0.024935756
386.75 2015-01-08 12:30:00 UTC 0.035052558
386.75 2015-01-08 13:00:00 UTC 0.031221485
386.75 2015-01-08 13:30:00 UTC 0.04346359
386.75 2015-01-08 14:00:00 UTC 0.045936727
387.17 2015-01-08 10:30:00 UTC 0.025224896
387.17 2015-01-08 12:30:00 UTC 0.034762997
387.17 2015-01-08 13:00:00 UTC 0.028572201
387.17 2015-01-08 13:30:00 UTC 0.042917018
387.17 2015-01-08 14:00:00 UTC 0.044149556
387.6 2015-01-08 10:30:00 UTC 0.025299836
387.6 2015-01-08 12:30:00 UTC 0.033927464
387.6 2015-01-08 13:00:00 UTC 0.028148562
387.6 2015-01-08 13:30:00 UTC 0.041902329
387.6 2015-01-08 14:00:00 UTC 0.044349387
388.02 2015-01-08 10:30:00 UTC 0.025739224
388.02 2015-01-08 12:30:00 UTC 0.034077479
388.02 2015-01-08 13:00:00 UTC 0.027567832
388.02 2015-01-08 13:30:00 UTC 0.041084088
388.02 2015-01-08 14:00:00 UTC 0.043637286
388.44 2015-01-08 10:30:00 UTC 0.025029961
388.44 2015-01-08 12:30:00 UTC 0.033231969
388.44 2015-01-08 13:00:00 UTC 0.027399323
388.44 2015-01-08 13:30:00 UTC 0.040655078
388.44 2015-01-08 14:00:00 UTC 0.043807616
388.87 2015-01-08 10:30:00 UTC 0.024874652
388.87 2015-01-08 12:30:00 UTC 0.033941312
388.87 2015-01-08 13:00:00 UTC 0.026494352
388.87 2015-01-08 13:30:00 UTC 0.039842939
388.87 2015-01-08 14:00:00 UTC 0.042183946
389.29 2015-01-08 10:30:00 UTC 0.024026924
389.29 2015-01-08 12:30:00 UTC 0.03308266
389.29 2015-01-08 13:00:00 UTC 0.02476139
389.29 2015-01-08 13:30:00 UTC 0.038915812
389.29 2015-01-08 14:00:00 UTC 0.041041478
389.71 2015-01-08 10:30:00 UTC 0.024493304
389.71 2015-01-08 12:30:00 UTC 0.033378314
389.71 2015-01-08 13:00:00 UTC 0.02457211
389.71 2015-01-08 13:30:00 UTC 0.038083439
389.71 2015-01-08 14:00:00 UTC 0.040543933
390.14 2015-01-08 10:30:00 UTC 0.023958464
390.14 2015-01-08 12:30:00 UTC 0.031807848
390.14 2015-01-08 13:00:00 UTC 0.024314877
390.14 2015-01-08 13:30:00 UTC 0.036944208
390.14 2015-01-08 14:00:00 UTC 0.038468215
390.56 2015-01-08 10:30:00 UTC 0.023415236
390.56 2015-01-08 12:30:00 UTC 0.030656805
390.56 2015-01-08 13:00:00 UTC 0.023315433
390.56 2015-01-08 13:30:00 UTC 0.035747324
390.56 2015-01-08 14:00:00 UTC 0.037748385
390.98 2015-01-08 10:30:00 UTC 0.02364786
390.98 2015-01-08 12:30:00 UTC 0.029974454
390.98 2015-01-08 13:00:00 UTC 0.022323168
390.98 2015-01-08 13:30:00 UTC 0.03559911
390.98 2015-01-08 14:00:00 UTC 0.036798512
391.41 2015-01-08 10:30:00 UTC 0.023615735
391.41 2015-01-08 12:30:00 UTC 0.029215432
391.41 2015-01-08 13:00:00 UTC 0.022486032
391.41 2015-01-08 13:30:00 UTC 0.035064774
391.41 2015-01-08 14:00:00 UTC 0.036922789
391.83 2015-01-08 10:30:00 UTC 0.023886311
391.83 2015-01-08 12:30:00 UTC 0.030276941
391.83 2015-01-08 13:00:00 UTC 0.022030923
391.83 2015-01-08 13:30:00 UTC 0.035458087
391.83 2015-01-08 14:00:00 UTC 0.037450268
392.25 2015-01-08 10:30:00 UTC 0.023663435
392.25 2015-01-08 12:30:00 UTC 0.029819682
392.25 2015-01-08 13:00:00 UTC 0.022638028
392.25 2015-01-08 13:30:00 UTC 0.036372675
392.25 2015-01-08 14:00:00 UTC 0.03837374
392.68 2015-01-08 10:30:00 UTC 0.024106285
392.68 2015-01-08 12:30:00 UTC 0.031880794
392.68 2015-01-08 13:00:00 UTC 0.023939118
392.68 2015-01-08 13:30:00 UTC 0.038339545
392.68 2015-01-08 14:00:00 UTC 0.040665343
393.1 2015-01-08 10:30:00 UTC 0.024691749
393.1 2015-01-08 12:30:00 UTC 0.032765706
393.1 2015-01-08 13:00:00 UTC 0.025538355
393.1 2015-01-08 13:30:00 UTC 0.040027871
393.1 2015-01-08 14:00:00 UTC 0.042256898
393.53 2015-01-08 10:30:00 UTC 0.025101871
393.53 2015-01-08 12:30:00 UTC 0.034006205
393.53 2015-01-08 13:00:00 UTC 0.025626816
393.53 2015-01-08 13:30:00 UTC 0.040520664
393.53 2015-01-08 14:00:00 UTC 0.043067286
393.95 2015-01-08 10:30:00 UTC 0.02553642
393.95 2015-01-08 12:30:00 UTC 0.033935589
393.95 2015-01-08 13:00:00 UTC 0.025986827
393.95 2015-01-08 13:30:00 UTC 0.040955645
393.95 2015-01-08 14:00:00 UTC 0.043140914
394.37 2015-01-08 10:30:00 UTC 0.025124136
394.37 2015-01-08 12:30:00 UTC 0.03394605
394.37 2015-01-08 13:00:00 UTC 0.025500373
394.37 2015-01-08 13:30:00 UTC 0.040274572
394.37 2015-01-08 14:00:00 UTC 0.042235067
394.8 2015-01-08 10:30:00 UTC 0.025047369
394.8 2015-01-08 12:30:00 UTC 0.033224756
394.8 2015-01-08 13:00:00 UTC 0.026189009
394.8 2015-01-08 13:30:00 UTC 0.039846411
394.8 2015-01-08 14:00:00 UTC 0.041396087
395.22 2015-01-08 10:30:00 UTC 0.02453564
395.22 2015-01-08 12:30:00 UTC 0.032852577
395.22 2015-01-08 13:00:00 UTC 0.025478007
395.22 2015-01-08 13:30:00 UTC 0.038725719
395.22 2015-01-08 14:00:00 UTC 0.040675044
395.64 2015-01-08 10:30:00 UTC 0.024172006
395.64 2015-01-08 12:30:00 UTC 0.03143403
395.64 2015-01-08 13:00:00 UTC 0.025283389
395.64 2015-01-08 13:30:00 UTC 0.037983879
395.64 2015-01-08 14:00:00 UTC 0.040505154
396.07 2015-01-08 10:30:00 UTC 0.023772586
396.07 2015-01-08 12:30:00 UTC 0.030891897
396.07 2015-01-08 13:00:00 UTC 0.023739945
396.07 2015-01-08 13:30:00 UTC 0.036564522
396.07 2015-01-08 14:00:00 UTC 0.038996148
396.49 2015-01-08 10:30:00 UTC 0.023877002
396.49 2015-01-08 12:30:00 UTC 0.030795438
396.49 2015-01-08 13:00:00 UTC 0.02486322
396.49 2015-01-08 13:30:00 UTC 0.03694381
396.49 2015-01-08 14:00:00 UTC 0.0383815
396.91 2015-01-08 10:30:00 UTC 0.023956595
396.91 2015-01-08 12:30:00 UTC 0.030401715
396.91 2015-01-08 13:00:00 UTC 0.024762964
396.91 2015-01-08 13:30:00 UTC 0.036871622
396.91 2015-01-08 14:00:00 UTC 0.037477143
397.34 2015-01-08 10:30:00 UTC 0.024049071
397.34 2015-01-08 12:30:00 UTC 0.030112019
397.34 2015-01-08 13:00:00 UTC 0.024489802
397.34 2015-01-08 13:30:00 UTC 0.036308702
397.34 2015-01-08 14:00:00 UTC 0.036848074
397.76 2015-01-08 10:30:00 UTC 0.02353935
397.76 2015-01-08 12:30:00 UTC 0.02969331
397.76 2015-01-08 13:00:00 UTC 0.023213298
397.76 2015-01-08 13:30:00 UTC 0.034660694
397.76 2015-01-08 14:00:00 UTC 0.035876086
398.18 2015-01-08 10:30:00 UTC 0.023167681
398.18 2015-01-08 12:30:00 UTC 0.02832176
398.18 2015-01-08 13:00:00 UTC 0.022235355
398.18 2015-01-08 13:30:00 UTC 0.033057638
398.18 2015-01-08 14:00:00 UTC 0.03529138
398.61 2015-01-08 10:30:00 UTC 0.02250628
398.61 2015-01-08 12:30:00 UTC 0.027267648
398.61 2015-01-08 13:00:00 UTC 0.021039857
398.61 2015-01-08 13:30:00 UTC 0.03160762
398.61 2015-01-08 14:00:00 UTC 0.033852105
399.03 2015-01-08 10:30:00 UTC 0.022272852
399.03 2015-01-08 12:30:00 UTC 0.025570091
399.03 2015-01-08 13:00:00 UTC 0.019853419
399.03 2015-01-08 13:30:00 UTC 0.02954859
399.03 2015-01-08 14:00:00 UTC 0.031920991
399.45 2015-01-08 10:30:00 UTC 0.021592502
399.45 2015-01-08 12:30:00 UTC 0.024097952
399.45 2015-01-08 13:00:00 UTC 0.018753267
399.45 2015-01-08 13:30:00 UTC 0.027751242
399.45 2015-01-08 14:00:00 UTC 0.030136467
399.88 2015-01-08 10:30:00 UTC 0.021099994
399.88 2015-01-08 12:30:00 UTC 0.022781147
399.88 2015-01-08 13:00:00 UTC 0.01775552
399.88 2015-01-08 13:30:00 UTC 0.026459102
399.88 2015-01-08 14:00:00 UTC 0.028930313
7

I sent a part of my dataset @nirgrahamuk

8

...you've supplied an example in a difficult way (non trivial to get into an R session). and you haven't said how this relates to your image ...

9

Hi, @nirgrahamuk ! I would like to calculate the area under the line and above as shown in the image, using my data. Thanks!

10

Dear Arthurt,
How can I find automatically the function of the solid black line. I searched for that pracma package. I found this link: trapz function - RDocumentation
According to this link, I think I need to use trapzfun. Is there any example to use that? I am sorry I am new to using that.
Thanks!

11

The function of the black line must come from your own work. I don't know anything about your particular application :slight_smile:

If the black line is something that exists as data, you can supply vectors of x and y values to trapz.

If the black line is something that exists as a formula, you can define a range of x values and use the formula to calculate a y value for each one, and supply these to trapz.

12

This is much like calculating peak areas in chromatography. My guess is that rg30 is the height of the peak. Find the interval between measurements. Multiply the height by interval and take the sum. In the graph provided the baseline is at zero before and after the "peak." It will take more work if peaks overlap. Try looking at all the methods for something like gas chromatography, probably out of the 1960s or so (or whenever this was done by hand rather than packaged up into the software). For the record, this is the graphical approach to integration which was suggested before. If you had an equation the idea would be to find the area as the width of the interval between measurements goes to zero.

14

The Area Under the ROC curve (AUC) is an aggregated metric that evaluates how well a logistic regression model classifies positive and negative outcomes at all possible cutoffs

Key words - logistic regression. Your data implies continuous variables, whether true or predicted, we cannot get the AUC for a logistic regression. You need a linear regression

16

What is c:/users/cragg/onedrive/desktop/data.csv ?
I dont have that..

May I suggest that you try to avoid being rude ?

17

I think you may be confusing the AUC statistic which is the are under the ROC curve with areas under curve more generally, see integrals : Area under curve - Wikipedia

p.s. ROC curves are not reserved for Linear regressions and logistic regressions can be analysed through that lense also.

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19

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