how to add best fit line in subplots in function plotmatrix?

Data = readtable('autompg.csv', 'VariableNamingRule','preserve');
Displacement = Data.displacement;
Horsepower = Data.horsepower;
Weight = Data.weight;
Acceleration = Data.acceleration;

% Add row and column labels
variableNames = {'Displacement', 'Horsepower', 'Weight', 'Acceleration'};

Predictors = [Displacement, Horsepower, Weight, Acceleration];
[S,AX,BigAx,H,HAx] = plotmatrix(Predictors)

iterations = size(AX,1);
for i = 1:iterations
    for j = 1:iterations
        if i ~= j
            % Overlay best fit line
            ax = AX(i, j);

            % Add correlation value
            corr_val = corr_matrix(i, j);
            text(ax, 0.5, 0.9, sprintf('r = %.3f', corr_val), ...
                'Units', 'normalized', 'HorizontalAlignment', 'center');
        end
    end
end

% Add labels
for i = 1:iterations
    AX(i,1).YLabel.String = variableNames(i);
    AX(iterations,i).XLabel.String = variableNames(i);
end


Right now the above code shows the image below using the function plotmatrix 

however I want this to look like the second one where there is the best fit line in each subplots. Please note the second image
uses the function corrplot. 

[NAFISA SIDDIQUI]

i tried doing this but there is error

iterations = size(AX,1);
for i = 1:iterations
    for j = 1:iterations
        if i ~= j
            % Overlay best fit line
            ax = AX(i, j);

   xdata = Predictors(:, i); 
   ydata = Predictors(:, j); 
   p = polyfit(xdata, ydata, 1); 
   hold(ax, 'on');  
   plot(ax, xdata, polyval(p, xdata), 'r--');

Answer 1

[Shubham]

Hi Nafisa,

The code snippet you've shared is almost correct in its approach to overlay a best fit line on each subplot generated by plotmatrix. However, it seems like you're missing a crucial part where you calculate the correlation matrix (corr_matrix) that you're trying to use later for annotating the plots. Additionally, the way you're attempting to overlay the best fit line is correct, but let's ensure it's integrated properly into your loop.

Here's a revised version of your code that includes the calculation of the correlation matrix and ensures that the best fit lines are correctly added to each subplot:

Data = readtable('autompg.csv', 'VariableNamingRule','preserve');
Displacement = Data.displacement;
Horsepower = Data.horsepower;
Weight = Data.weight;
Acceleration = Data.acceleration;

% Add row and column labels
variableNames = {'Displacement', 'Horsepower', 'Weight', 'Acceleration'};
Predictors = [Displacement, Horsepower, Weight, Acceleration];

% Calculate correlation matrix for later use
corr_matrix = corr(Predictors, 'Rows', 'complete');

[S,AX,BigAx,H,HAx] = plotmatrix(Predictors);
iterations = size(AX,1);

for i = 1:iterations
    for j = 1:iterations
        if i ~= j
            % Overlay best fit line
            ax = AX(i, j);
            xdata = Predictors(:, j); % Note: The columns (j) should match x-axis in plotmatrix
            ydata = Predictors(:, i); % Note: The rows (i) should match y-axis in plotmatrix
            p = polyfit(xdata, ydata, 1); % Fit line
            hold(ax, 'on');  
            plot(ax, xdata, polyval(p, xdata), 'r--'); % Plot line
            
            % Add correlation value
            corr_val = corr_matrix(i, j);
            text(ax, 0.5, 0.9, sprintf('r = %.3f', corr_val), ...
                'Units', 'normalized', 'HorizontalAlignment', 'center', 'FontSize', 8);
            hold(ax, 'off'); % Release hold to allow next plots
        end
    end
end

% Add labels
for i = 1:iterations
    AX(i,1).YLabel.String = variableNames{i};
    AX(iterations,i).XLabel.String = variableNames{i};
end

Key modifications and clarifications:

• Before looping through the axes to add best fit lines and correlation values, calculate the correlation matrix of your predictors. This matrix is then used within the loop to annotate each subplot with the corresponding correlation coefficient.
• When extracting xdata and ydata for fitting the line, ensure that you're using the correct indices. The outer loop variable i should index ydata, and the inner loop variable j should index xdata, matching how plotmatrix organizes the subplots.
• The hold(ax, 'on') command is correctly applied to ensure that the line plot is added on top of the existing scatter plot. After plotting the line, hold(ax, 'off') is used to release the hold state, though it's not strictly necessary at the end of your plotting commands for each subplot.

This revised code should overlay a best fit line on each of the off-diagonal plots in your plotmatrix output and annotate them with the correlation coefficient, closely aligning with the functionality you described.

[NAFISA SIDDIQUI]

Thank you so very much Shubham, the code definitely worked!! and looks like this

however i was wondering if we could extend the line so that it crosses the y intercept so I tried using this code

for i = 1:iterations
    for j = 1:iterations
        if i ~= j
            % Overlay best fit line
            ax = AX(i, j);
            xdata = Predictors(:, j); % Note: The columns (j) should match x-axis in plotmatrix
            ydata = Predictors(:, i); % Note: The rows (i) should match y-axis in plotmatrix
            p = polyfit(xdata, ydata, 1); % Fit line
            
            % Extend the best fit line
            x_limits = xlim(ax);
            y_limits = ylim(ax);
            x_min = x_limits(1);
            x_max = x_limits(2);
            y_min = polyval(p, x_min);
            y_max = polyval(p, x_max);
            
            % Plot extended line
            hold(ax, 'on');
            plot(ax, [x_min, x_max], [y_min, y_max], 'r');
            
            % Add correlation value
            corr_val = corr_matrix(i, j);
            text(ax, 0.5, 0.9, sprintf('r = %.3f', corr_val), ...
                'Units', 'normalized', 'HorizontalAlignment', 'center', 'FontSize', 8);
            hold(ax, 'off'); % Release hold to allow next plots
        end
    end
end

this above code gives this image

however when I use the function corrplot it gives an image like the one below so does that mean there is something wrong with my code?