Create trendline for a plot of a set of disordered data? - matlab

Question

I have a totally random set of data with around 500 inputs obtained from a physics experiment in excel format. I plotted it successfully but I am not able to create a trendline for my plot. I need to find the trendline for this data.
excel data can be found from this google drive link.
Alternatively, these are the first 2 columns of the Excel file:
0_x 0_y
0.321816 -82.594828
1.595041 -85.396122
2.868266 -82.085502
3.632201 -84.632133
4.905426 -83.868143
6.178651 -84.122807
7.197231 -85.905448
7.961166 -84.37747
8.470457 -85.141459
9.743682 -82.340165
10.252972 -84.886796
11.271552 -82.594828
13.054067 -84.886796
13.054067 -83.104154
14.327292 -84.632133
15.345872 -86.160112
16.364452 -84.886796
17.383032 -86.160112
18.401612 -83.868143
19.165547 -85.905448
20.438773 -82.849491
21.457353 -85.396122
22.221288 -83.104154
22.475933 -85.650785
23.494513 -85.650785
24.513093 -84.632133
25.277028 -85.141459
26.550253 -84.122807
27.314188 -85.141459
28.587413 -82.849491
29.860638 -84.886796
31.133864 -82.340165
31.897799 -84.886796
32.916379 -83.868143
33.934959 -84.37747
34.698894 -84.886796
35.717474 -84.122807
37.245344 -85.141459
38.263924 -83.104154
39.282504 -84.122807
40.301084 -81.576175
40.810374 -84.122807
42.0836 -82.085502
43.356825 -84.886796
44.12076 -85.396122
45.13934 -85.141459
45.903275 -86.669438
47.1765 -84.632133
47.940435 -85.396122
48.70437 -83.358817
49.977595 -85.396122
50.486885 -82.085502
51.25082 -84.632133
52.2694 -83.868143
52.524045 -83.868143
53.287981 -85.905448
55.070496 -84.37747
56.343721 -86.160112
57.107656 -84.122807
57.871591 -86.160112
58.635526 -83.61348
59.144816 -85.905448
60.163396 -84.122807
61.181976 -85.396122
62.709846 -86.160112
62.964491 -85.396122
64.492362 -86.669438
65.001652 -85.141459
65.765587 -85.905448
66.784167 -84.122807
68.566682 -86.160112
69.585262 -83.358817
70.349197 -85.650785
71.113132 -84.37747
72.386357 -84.632133
73.150292 -85.141459
73.914227 -83.868143
74.932807 -85.141459
75.951388 -82.594828
77.224613 -85.396122
78.752483 -82.340165
79.516418 -85.141459
80.280353 -84.122807
81.553578 -85.905448
82.317513 -85.650785
82.826803 -84.886796
83.845383 -85.905448
83.336093 -83.868143
81.808223 -85.905448
80.534998 -83.104154
79.516418 -85.905448
78.497838 -83.868143
76.969968 -85.396122
75.696743 -86.160112
74.678162 -85.396122
73.659582 -86.669438
72.641002 -85.141459
71.367777 -86.160112
69.585262 -83.61348
68.566682 -86.160112
67.548102 -84.122807
66.274877 -86.160112
65.765587 -85.650785
65.001652 -85.905448
63.728426 -86.414775
61.945911 -84.632133
60.927331 -86.160112
60.418041 -83.61348
59.144816 -85.905448
58.380881 -82.594828
57.362301 -84.886796
56.089076 -82.849491
55.325141 -85.141459
54.561206 -85.141459
53.797271 -83.61348
52.524045 -85.141459
51.505465 -83.358817
50.486885 -85.141459
49.21366 -83.104154
48.19508 -84.886796
47.431145 -82.340165
46.15792 -84.886796
45.13934 -84.37747
44.12076 -85.396122
42.847535 -85.141459
41.319664 -84.886796
40.301084 -85.396122
39.537149 -84.632133
38.009279 -85.905448
37.245344 -82.849491
35.972119 -85.396122
34.953539 -83.868143
34.189604 -85.141459
32.152444 -84.632133
31.388509 -84.632133
30.115283 -86.160112
29.351348 -83.61348
28.078123 -85.396122
27.568833 -82.594828
26.804898 -85.396122
25.786318 -82.085502
24.513093 -85.141459
23.494513 -85.141459
22.730578 -84.37747
21.711998 -84.632133
20.438773 -84.122807
19.674838 -84.632133
18.401612 -82.594828
17.383032 -84.886796
16.619097 -82.594828
15.855162 -84.122807
15.091227 -83.61348
13.818002 -84.122807
12.799422 -84.122807
11.780842 -84.122807
11.016907 -84.886796
9.743682 -82.849491
8.215811 -84.632133
7.706521 -81.830838
6.942586 -84.632133
5.414716 -83.868143
4.141491 -85.396122
3.122911 -85.396122
2.358976 -84.886796
1.085751 -85.905448
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-70.469501 -82.085502
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-67.92305 -83.104154
-67.41376 -85.396122
-66.649825 -85.141459
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-6.04431 -86.414775
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-4.00715 -83.868143
-2.479279 -85.396122
-1.206054 -82.849491
-0.696764 -85.396122
-0.187474 -83.868143
1.085751 -86.160112
1.849686 -86.160112
3.122911 -85.905448
4.141491 -86.414775
4.905426 -84.632133
5.924006 -86.160112
6.178651 -83.358817
7.197231 -85.905448
8.215811 -82.594828
9.234392 -85.141459
10.252972 -84.632133
11.271552 -84.632133
13.054067 -85.396122
13.563357 -84.122807
14.836582 -85.141459
15.855162 -83.868143
I tried polyval, polyfit, Basic fitting (plot->tootls->basic fitting)
datasheet=xlsread('08_08_2019-11_08_58_.xlsx','Worksheet');
x=datasheet(:,1);
y=datasheet(:,2);
plot(x,y)

Answer 1

What exactly do you understand under trendline? A linear line p1*x+p2 can be achieved by the following code, which assumes that you have the curve fitting toolbox installed. The last part concerning polyfit() does not need this toolbox.
If you check these (fit) and these (fitoptions) docs, you'll find out that also other options, for quadratic polynomials, exponentials or fourier/sin-cos functions (and many more) are available when using the toolbox. The xand y of the data you posted looks like sinusoidal to me, so I'd go with the second option below.
Linear fit p1*x+p2
data = xlsread('08_08_2019-11_08_58_.xlsx');
x=data(:,1);
y=data(:,2);
[xData, yData] = prepareCurveData(x, y);
% Set up fittype and options.
ft = fittype('poly1')
% Fit model to data.
[fitresult, gof] = fit(xData, yData, ft);
% Plot fit with data.
figure
h = plot(fitresult, xData, yData);
legend(h, 'data', 'linear 1st order polynomial', 'Location', 'NorthEast');
xlabel('x'); ylabel('y'); grid on
% Extract the equation(ft) and the coefficients
coeffnames(fitresult)
coeffvalues(fitresult)
Using a Nonlinear Least Squares to fit a Fourier model a0 + a1*cos(x*w) + b1*sin(x*w)
data = xlsread('08_08_2019-11_08_58_.xlsx');
x=data(:,1);
y=data(:,2);
[xData, yData] = prepareCurveData(x, y);
% Set up fittype and options.
ft = fittype('fourier1')
opts = fitoptions('Method', 'NonlinearLeastSquares');
% Fit model to data.
[fitresult, gof] = fit(xData, yData, ft, opts);
% Plot fit with data.
figure
h = plot(fitresult, xData, yData);
legend(h, 'data', 'Fourier model fit', 'Location', 'NorthEast');
xlabel('x'); ylabel('y'); grid on
% Extract the equation(ft) and the coefficients
coeffnames(fitresult)
coeffvalues(fitresult)
Using the polyfit() and polyval() functions for p1*x+p2:
% using polyfit and polyval (no toolbox needed)
data = xlsread('08_08_2019-11_08_58_.xlsx');
x=data(:,1);
y=data(:,2);
p = polyfit(x, y, 1)
pp = polyval(p, x);
h = plot(x, y, 'o', x, pp);
legend(h, 'data', 'linear 1st order polynomial', 'Location', 'NorthEast');
xlabel('x'); ylabel('y'); grid on
Without Curve fitting toolbox, using your mentioned in-plot method
data = xlsread('08_08_2019-11_08_58_.xlsx');
x=data(:,1);
y=data(:,2);
plot(x, y)
In the figure window: Tools -> Basic Fitting -> linear/polynomial
also seems to work for your given case.