Try this:
% Fits a Gaussian to the USA daily deaths for CoVid-19, which includes data for only the left portion of the Gaussian, not the full Gaussian.
%--------------------------------------------------------------------------------------------------------------------------------------------------------
% CLEAN UP - INITIALIZATION STEPS
clc; % Clear the command window.
fprintf('Beginning to run %s.m.\n', mfilename);
close all; % Close all figures (except those of imtool.)
clearvars; % Erase all existing variables.
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
%--------------------------------------------------------------------------------------------------------------------------------------------------------
% TRAINING DATA PREPARATION
% Read in data from workbook.
data = readmatrix('Fitnlm_Gaussian_CoVid19.xlsx');
% Get rid of nans
validRows = ~isnan(data(:, 2));
% Get rid of zero counts
validRows = validRows & (data(:, 2) > 0);
data = data(validRows, :)
X = data(:, 1);
Y = data(:, 2);
hFig = figure;
plot(X, Y, 'b.-', 'LineWidth', 2, 'MarkerSize', 30);
grid on;
xlabel('Date', 'FontSize', fontSize);
ylabel('Daily Deaths', 'FontSize', fontSize);
title('CoVid-19 Daily Deaths', 'FontSize', fontSize);
% Make x axis be dates.
datetick('x', 'mmm dd, yyyy', 'keepticks');
ax = gca;
ax.XTickLabelRotation = -45;
% Convert X and Y into a table, which is the form fitnlm() likes the input data to be in.
tbl = table(X(:), Y(:));
%--------------------------------------------------------------------------------------------------------------------------------------------------------
% MODEL DEFINITION
% Define the model as Y = a + b * exp(-(x - c)^2 / d)
% Create an anonymous function for it.
% Note how this "x" of ModelFunction is related to big X and big Y.
% x((:, 1) is actually X and x(:, 2) is actually Y - the first and second columns of the table.
ModelFunction = @(b, x) b(1) + b(2) * exp(-(x(:, 1) - b(3)).^2/b(4));
%--------------------------------------------------------------------------------------------------------------------------------------------------------
% MODEL CREATION : ESTIMATION OF PARAMETERS
% Guess starting model values to start with. Just make your best guess.
% These are just starting points for the coefficients and will be adjusted during the fit to produce the real coefficients.
beta0 = [0, max(X), mean(X), var(X)]; % A guess at what the coefficients will be.
% Now the next line is where the actual model computation is done.
mdl = fitnlm(tbl, ModelFunction, beta0);
% Now the model creation is done and the coefficients have been determined.
% YAY!!!!
% Extract the coefficient values from the the model object.
% The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode.
coefficients = mdl.Coefficients{:, 'Estimate'}
%--------------------------------------------------------------------------------------------------------------------------------------------------------
% MODEL PLOTTING : PLOTTING FITTED/ESTIMATED VALUES OVER THE WHOLE RANGE OF X.
% Let's do a fit, but let's get more points on the fit, beyond just the widely spaced training points,
% so that we'll get a much smoother curve.
xFitted = linspace(min(X), max(X), 1920); % Let's use 1920 points, which will fit across an HDTV screen about one sample per pixel.
% Create smoothed/regressed data using the model:
yFitted = ModelFunction(coefficients, xFitted(:));
% yFitted = coefficients(1) + coefficients(2) * exp(-(xFitted - coefficients(3)).^2 / coefficients(4));
% Now we know that since it's a Gaussian there should not be any negative values. So clip to 0
yFitted = max(0, yFitted);
% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.
hold on;
plot(xFitted, yFitted, 'r-', 'LineWidth', 2);
grid on;
title('CoVid-19 Daily Deaths in the USA -- Exponential Regression with fitnlm()', 'FontSize', fontSize);
% Put a line at the peak.
darkGreen = [0, 0.5, 0];
xline(coefficients(3), 'Color', darkGreen, 'LineWidth', 3);
% Put up text for the green line.
str = sprintf(' Peak at %s', datestr(coefficients(3)));
text(coefficients(3), 100, str, 'Color', darkGreen, 'FontSize', 14, 'FontWeight', 'bold');
legendHandle = legend('Actual Y', 'Fitted Y', 'Location', 'northwest');
legendHandle.FontSize = 25;
hFig.WindowState = 'maximized';
fprintf('Done running %s.m.\n', mfilename);
