Finding the slope after drawing a trend/linear fit

I have an excel data. I want to find the slope after fitting a linear fit on it. In the attached plot, I manually drawn the fit line in black, I need the matlab code for it. So that the program will do it. I've attached my data too.

Answer 1

[Star Strider]

Alternatively —

files = dir('*.xlsx');
T1 = readtable(files.name)

T1 = 5001×2 table
       T          x    
    _______    ________

          0     0.04851
      4e-06    0.051774
      8e-06    0.050142
    1.2e-05     0.04851
    1.6e-05     0.04851
      2e-05    0.050142
    2.4e-05    0.050142
    2.8e-05    0.050142
    3.2e-05    0.050142
    3.6e-05    0.050142
      4e-05    0.050142
    4.4e-05    0.051774
    4.8e-05     0.04851
    5.2e-05    0.051774
    5.6e-05    0.051774
      6e-05    0.050142

VN = T1.Properties.VariableNames;

T = T1.T;
x = T1.x;

[xmax,idx] = max(x);
idxrng = 1:idx;

DM = [T(idxrng) ones(size(x(idxrng)))];                             % Design Matrix
B = DM \ x(idxrng)                                                  % Another Option Is 'polyfit'

B = 2×1

84.3962 0.0217

FitLine = DM * B;                                                   % Use 'polyval' With 'polyfit' 

xr(1) = 0.004;
yr(1) = [xr 1] * B;
yr(2) = 0.2;
xr(2) = (yr(2)-B(2))/B(1);

figure
plot(T,x)
hold on
plot(T(idxrng), FitLine, '-k', 'LineWidth',3)
plot([1 1]*xr(1), [yr(1) yr(2)], '-r')
plot([xr(1) xr(2)], [1 1]*yr(2), '-r')
hold off
grid
xlabel(VN{1})
ylabel(VN{2})
text(xr(1), yr(2), sprintf('\\uparrow\nSlope = %.2f', B(1)), 'Horiz','left', 'Vert','top')

.

[Reji G]

Thank you..... But this code works only for the excel data attached(D.xlsx). I want the code to be applied for any data set. How to generalize it ? I tried with few more data sets, and the fit itsef is wrongly plotting.

[Star Strider]

My pleasure.

I need to have the data set to work with, and know what you want to do with it.

[Reji G]

I've updated excel sheet with required data. T is common. Plot T&w, T&x, T&y, T&z. I want to draw a fit in increasing direction in the positive half cycles(As shown in the previous diagram) and the slope between each fit lines drawn for T&w, T&x, T&y, T&z.

[Star Strider]

If you want regression lines for the outset of each variable, this works —

files = dir('*.xlsx');
T1 = readtable(files.name)

T1 = 5001×5 table
       T          w            x            y             z     
    _______    ________    _________    __________    __________

          0     0.04851    -0.047776     -0.066858     0.0019753
      4e-06    0.051774     -0.04288     -0.063591    0.00034241
      8e-06    0.050142    -0.046144     -0.057056     0.0019753
    1.2e-05     0.04851    -0.047776     -0.052155    0.00034241
    1.6e-05     0.04851    -0.046144     -0.047254     0.0019753
      2e-05    0.050142    -0.044512     -0.042353     0.0036082
    2.4e-05    0.050142    -0.046144     -0.035819     0.0019753
    2.8e-05    0.050142    -0.046144     -0.027651     0.0019753
    3.2e-05    0.050142    -0.047776      -0.02275     0.0019753
    3.6e-05    0.050142    -0.044512     -0.019483    0.00034241
      4e-05    0.050142    -0.044512     -0.012948    0.00034241
    4.4e-05    0.051774    -0.046144    -0.0047799     0.0019753
    4.8e-05     0.04851    -0.046144    -0.0015127     0.0036082
    5.2e-05    0.051774    -0.047776     0.0033882     0.0019753
    5.6e-05    0.051774    -0.046144     0.0099227    0.00034241
      6e-05    0.050142    -0.044512      0.018091     0.0052411

VN = T1.Properties.VariableNames;

T = T1.T;

figure
tiledlayout(2,2)
for k = 1:size(T1,2)-1
    nexttile
    v = T1{:,k+1};
    plot(T, v)
    grid
    title(VN{k+1})
    [vmax,idx] = max(v);
    idxrng = 1:idx;

    DM = [T(idxrng) ones(size(T(idxrng)))];                             % Design Matrix
    B = DM \ v(idxrng);                                                 % Another Option Is 'polyfit'
    FitLine = DM * B;                                                   % Use 'polyval' With 'polyfit' 
       
    hold on
    plot(T(idxrng), FitLine, '-k', 'LineWidth',3)
    hold off
    xlabel(VN{1})
    ylabel(VN{k+1})
    text(mean(xlim), 0.9*max(ylim), sprintf('Regression Line Slope = %.3f',B(1)), 'Horiz','center', 'Vert','top')
 end

The regression lines do not connect the first and first maximum points in all variables because they are fitting all the data between those points. If you want something else, plese be specific.

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