I want the equation of a graph data.

M=[0                       0    
93.07876          0.224404    
186.1575          0.476858    
262.5298          0.729313    
303.1026          0.869565    
310.2625          1.290323    
319.8091          1.598878    
329.3556          1.486676    
341.2888          1.318373    
353.222          1.542777    
362.7685          1.851332    
372.315          2.103787    
377.0883          2.412342   
381.8616          2.664797    
386.6348          2.889201    
391.4081          3.169705    
396.1814          3.45021    
400.9547          3.702665    
408.1146          3.98317    
410.5012          4.235624    
415.2745          4.460028    
420.0477          4.712482    
424.821          4.964937    
446.3007          5.021038    
467.7804          5.105189    
477.327          5.329593    
484.4869          5.553997    
494.0334          5.778401    
501.1933          5.946704    
508.3532          6.143058    
515.5131          6.367461    
522.673             6.563815    
529.8329          6.788219    
536.9928          7.040673    
544.1527          7.265077    
548.926          7.517532    
556.0859          7.798036    
565.6325          8.078541    
572.7924          8.387097    
579.9523          8.695652    
589.4988          9.004208    
594.2721          9.284712    
601.432          9.565217    
606.2053          9.817672    
613.3652          10.07013    
625.2983          9.901823    
637.2315          9.677419    
649.1647          9.509116    
663.4845          9.340813    
675.4177          9.11641    
684.9642          9.340813    
692.1241          9.565217    
696.8974          9.817672    
704.0573          10.07013    
706.4439          10.18233   
718.3771          10.26648    
720.7637          10.49088    
723.1504          10.63114    
725.537              10.79944    
727.9236          10.96774    
730.3103          11.1641    
732.6969          11.41655    
735.0835          11.64095    
737.4702          11.86536    
739.8568          12.08976    
742.2434          12.37027    
744.6301          12.62272    
747.0167          12.84712    
751.79          13.09958    
756.5632          13.29593   
 761.3365          13.54839    
766.1098          13.77279    
770.8831          13.99719    
775.6563          14.2216    
780.4296          14.446    
785.2029          14.69846    
789.9761          14.89481    
792.3628          15.11921    
797.136          15.28752    
801.9093          15.45582    
806.6826          15.68022    
811.4558          15.84853    
813.8425          16.10098    
818.6158          16.32539    
828.1623          16.63394    
830.5489          16.91445    
835.3222          17.13885    
840.0955          17.36325    
844.8687          17.64376    
852.0286          17.89621    
875.895          17.89621    
890.2148          17.89621    
902.148          17.89621    
918.8544          17.89621    
926.0143          17.89621    
933.1742          17.75596    
940.3341          17.58766    
947.494          17.3913    
952.2673          17.223    
954.6539          17.0547    
964.2005          16.91445    
971.3604          16.69004    
978.5203          16.46564    
985.6802          16.24123    
995.2267          15.98878    
1002.387          15.79243    
1009.547          15.53997    
1016.706          15.31557    
1028.64          15.03506    
1033.413          14.78261    
1035.8          14.5582    
1038.186          14.36185    
1040.573          14.1655    
1042.959          13.94109    
1045.346          13.74474   
1047.733          13.52034    
1050.119          13.32398    
1052.506          13.09958    
1054.893          12.90323    
1059.666          12.65077    
1062.053          12.39832    
1064.439          12.14586    
1069.212          11.80926    
1071.599          11.5568    
1076.372          11.3324    
1078.759          11.07994    
1083.532          10.85554    
1090.692          10.63114    
1097.852          10.32258    
1107.399          10.07013    
1109.785          9.873773   
1112.172          9.649369    
1114.558          9.453015    
1116.945          9.284712    
1114.558          9.088359    
1116.945          8.920056    
1116.945          9.11641    
1119.332          9.284712    
1121.718          9.453015    
1121.718          9.621318    
1121.718          9.789621    
1124.105          10.01403    
1124.105          10.21038    
1126.492          10.40673    
1133.652          10.40673    
1136.038          10.23843    
1138.425          10.09818    
1145.585          9.929874    
1145.585          9.70547    
1147.971          9.509116    
1147.971          9.284712    
1147.971          9.14446    
1152.745          8.948107    
1155.131          8.723703    
1157.518          8.499299    
1162.291          8.274895    
1167.064          7.99439    
1171.838          7.798036    
1171.838          7.573633    
1171.838          7.293128    
1176.611          7.040673    
1178.998          6.788219    
1181.384          6.591865    
1183.771          6.367461    
1186.158          6.171108    
1188.544          5.974755    
1190.931          5.778401    
1195.704          5.525947    
1198.091          5.357644    
1200.477          5.217391    
1200.477          5.077139    
1202.864          5.13324    
1202.864          5.301543    
1205.251          5.441795    
1202.864          5.553997    
1202.864          5.778401    
1202.864          6.030856    
1202.864          6.227209    
1205.251          6.395512    
1205.251          6.591865    
1205.251          6.84432    
1205.251          7.040673    
1207.637          7.237027    
1207.637          7.489481    
1210.024          7.657784    
1210.024          7.826087    
1214.797          7.826087    
1214.797          7.713885    
1214.797          7.573633    
1217.184          7.461431    
1217.184          7.293128    
1221.957          7.096774    
1221.957          6.816269    
1226.73          6.619916    
1229.117          6.367461    
1231.504          6.143058    
1243.437          6.058906    
1245.823          5.890603    
1248.21          5.638149    
1252.983          5.385694    
1252.983          5.189341    
1255.37          4.908836    
1260.143          4.684432    
1260.143          4.460028    
1264.916          4.235624    
1267.303          4.01122    
1272.076          3.814867    
1276.85          3.955119    
1281.623          4.123422    
1286.396          4.235624    
1291.169          4.347826    
1295.943          4.431978    
1303.103          4.291725    
1305.489          4.123422    
1307.876          3.955119    
1310.263          3.786816    
1315.036          3.562412    
1315.036          3.281907    
1315.036          3.057504    
1319.809          2.8331    
1317.422          2.524544    
1319.809          2.215989    
1322.196          1.991585    
1322.196          1.71108    
1324.582          1.514727    
1324.582          1.234222    
1324.582          1.009818    
1329.356          1.093969    
1334.129          1.262272    
1338.902          1.430575    
1343.675          1.654979    
1348.449          1.823282    
1353.222          1.963534    
1357.995          2.103787    
1362.768          2.215989    
1367.542          2.328191    
1372.315          2.131837    
1372.315          1.935484    
1379.475          1.767181    
1381.862          1.598878    
1384.248          1.430575    
1386.635          1.262272    
1389.021          1.093969    
1403.341          1.12202    
1420.048          1.206171    
1439.141          1.290323    
1460.621          1.374474    
1477.327          1.430575    
1486.874          1.430575    
498.807          1.234222    
1510.74          1.037868    
1520.286          0.785414    
1529.833          0.56101    
1539.379          0.392707    
1548.926          0.252454    
553.699          0.112202    
1558.473          0   ];
plot(M(:,1),M(:,2),'o')

[Dyuman Joshi]

You've asked the same type of question many times now.

Why not use the methods suggested in the answers of previous questions?

[Chaudhary P Patel]

Actually, Last time i asked the process of getting the equation.

But, they just provide me equation with all constants.

That is why i am asking the same type question.

In last problem time step was same but in this data time step are different or irregular.

so please help me in getting the equation of the above data.

[Sam Chak]

@Chaudhary P Patel,

I've noticed that in your previous post, you might have missed exploring the application of certain curve-fitting tools in MATLAB to derive the equation. It seems your primary goal is obtaining the equation model that best fits the data, rather than delving into the intricacies of the curve-fitting tools themselves.

If I'm not mistaken, your future inquiries might also revolve around acquiring the equation rather than understanding the tools. Could we perhaps initiate the process by plotting the graph using the plot() function and analyzing the pattern? This approach could showcase your minimal effort while still achieving the desired outcome.

plot(x, y)

[Chaudhary P Patel]

Actually, Last time i asked the process of getting the equation.

But, they just provide me equation with all constants.

That is why i am asking the same type question.

In last problem time step was same but in this data time step are different or irregular.

so please help me in getting the equation of the above data.

Answer 1

[Sulaymon Eshkabilov]

Here is the answer code that I posted for your prevous post that works in the same way:

D = load('Patel_Data.txt');
[x, IDX] = sort(D(:,1));
y = D(IDX, 2);
yy = smoothdata(y, 'gaussian', 5);
plot(x,yy, 'b--', 'LineWidth', 2)
hold on
FUN = @(a, x) a(1) * exp(-((x - a(2)) / a(3)).^2);  % Gaussian model
a0 = [15; 777; 333];                                % Initial guess values for a
MODEL = fitnlm(x, yy, FUN, a0)

MODEL = 
Nonlinear regression model:
    y ~ F(a,x)

Estimated Coefficients:
          Estimate      SE       tStat       pValue   
          ________    _______    ______    ___________

    a1     16.505     0.16004    103.13    2.5842e-209
    a2     886.33      2.3362    379.39              0
    a3     334.76      3.5973     93.06    2.8802e-198


Number of observations: 257, Error degrees of freedom: 254
Root Mean Squared Error: 1.08
R-Squared: 0.953,  Adjusted R-Squared 0.953
F-statistic vs. zero model: 6.41e+03, p-value = 5.47e-239

plot(x, MODEL.Fitted, 'm-', 'LineWidth', 2);
legend('Data', 'Gaussian Fit Model')
grid on
xlabel('Time, [s]')
ylabel('Depth, [m]')

[Chaudhary P Patel]

This is ok sir,

but in the previous problem @Alexsha give the solution but how he did, he did not told. It was fit to the data.

Sir, for this i want the equation so that i can get the data with change time time steps.

Try the fitting function below:

Sum Squared Error (SSE): 1.05153845767184

Root of Mean Square Error (RMSE): 0.178507147609365

Correlation Coef. (R): 0.997415641383701

R-Square: 0.994837961676859

Parameter Best Estimate

--------- -------------

y0 -6.72273370419413

a1 13.5085640890228

b1 -7.32681575662562E-6

c1 1271.21138671474

a2 13.3029931198928

b2 -3.90619136753063E-6

c2 410.442920391101

a3 -3.56863630006966

b3 -6.4673256414225E-5

c3 896.221576681554

[Star Strider]

‘@Alexsha give the solution but how he did, he did not told.’

He does not use MATLAB. He uses a different (very expensive) optimisation software system.

Answer 2

[Steven Lord]

so please help me in getting the equation of the above data.

What makes you assume that there is a unique equation that fits that data? [That there is a "the equation"?]

x = 0:5;
y = zeros(size(x));
plot(x, y, 'o')

What is the unique equation that connects those six data points? Is it:

xfinergrid = 0:(1/16):5;
figure
plot(x, y, 'o');
p = 0;
hold on
plot(xfinergrid, polyval(p, xfinergrid), '-')
title('y = 0')

Or is it this?

figure
plot(x, y, 'o')
hold on
plot(xfinergrid, sinpi(xfinergrid), '-')
title('y = sin(\pi x)')

I can come up with an infinite number of curves that pass through those six points. So which one is "the right" one? Without more information it is literally impossible to decide.

[Sam Chak]

@Steven Lord, In the past, I queried several students who mentioned that their professors or supervisors had directed them to conduct experiments and gather data. Subsequently, they were tasked with identifying suitable equations to fit the data and publishing their findings as novel contributions.

Surprisingly, many of these students had not undergone any formal training in curve-fitting (including myself). They held the belief that specialized functions in MATLAB or Origin Pro (a software app renowned for its advanced graphing and data analysis capabilities) existed, enabling them to input the data into the application, which would then 'intelligently' provide the equation and coefficients that best fit the data.