Draw first principal component line and regression line on the same scatterplot
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Given the data below
WireLength DieHeight
1 125
4 110
5 287
6 200
8 350
10 280
12 400
14 370
13 480
18 420
19 540
22 518
where WireLength is the x axis and Die Height is the y axis
Draw a regression line and the first principal component line on the scatter plot.
Below I have standardized the data and then drew the scatterplot.
After this I drew the regression line using the code below
%regression best fit line
model = fitlm(WireLength_Z, DieHeight_Z);
p = polyfit(WireLength_Z, DieHeight_Z, 1);
f = polyval(p, WireLength_Z);
h = plot(WireLength_Z, DieHeight_Z,'ok', WireLength_Z, f, '-', 'LineWidth', 2, 'MarkerSize', 5)
%filled markers
set(h, {'MarkerFaceColor'}, get(h,'Color'));
% Set axis limits
xlim([-3.5 3.5]); % Set x-axis limits
ylim([-3.5 3.5]); % Set y-axis limits
% Add x and y axes
ax = gca; % Get current axes
ax.XAxisLocation = 'origin'; % Set x-axis to the origin
ax.YAxisLocation = 'origin'; % Set y-axis to the origin
ax.XColor = 'k'; % Set x-axis color
ax.YColor = 'k'; % Set y-axis color
% Add a grid for better visualization
grid on;
using this code my scatterplot now looks like
So on the same axis I also want to draw the first PC line only such that it looks something like
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Image Analyst
il 28 Ago 2024
It looks like you're doing a simple linear fit. I'm not seeing how you're using pca. It sounds like homework and they want you to compute the principal components, not simply do a fit with polyfit.
help pca
This is how I'd start it:
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format short g;
format compact;
fontSize = 16;
markerSize = 30;
% Define experimental/sample data.
% [WireLength, DieHeight]
data = [...
1 125
4 110
5 287
6 200
8 350
10 280
12 400
14 370
13 480
18 420
19 540
22 518]
% Plot the original data, which has 12 "observations".
figure('Name', 'PCA Demo by Image Analyst', 'NumberTitle', 'off')
subplot(2, 1, 1);
plot(data(:, 1), data(:, 2), 'b.', 'MarkerSize', markerSize)
title('Data in Original Coordinate Space', 'FontSize', fontSize)
xlabel('Wire Length', 'FontSize', fontSize)
ylabel('Die Height', 'FontSize', fontSize)
grid
% You can tell by looking at the plot that PC1 would go along
% the data from lower left to upper right. PC2 would then be
% the distance of the data perpendicularly from that line.
%--------------------------------------------------------
% Do a regression to minimize the squared vertical distance from the fitted line.
x = data(:, 1);
y = data(:, 2);
coefficients = polyfit(x, y, 1);
fittedx = [min(x), max(x)];
fittedy = polyval(coefficients, fittedx);
% Label points
for k = 1 : numel(x)
str = sprintf(' %d', k);
xt = x(k);
yt = y(k);
text(xt, yt, str, 'Color', 'b', 'FontSize', fontSize);
end
% Plot the regression over the original data
hold on;
plot(fittedx, fittedy, 'r-', 'LineWidth', 2);
legend('Original Data', 'Fitted Regression Line', 'Location', 'northwest')
drawnow;
%--------------------------------------------------------
% Do principal components analysis.
[coeff,score,latent,tsquared,explained,mu] = pca(data)
%--------------------------------------------------------
For a demo beyond that, see attached demo m-file, where I draw the axes on the original data.
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