matlab invalid expression error

Hi,

I am getting a lot of errors in my code, starting with line 24. Can someone please help me? Thanks!

clear, clc, close all

%%

set(0,'DefaultAxesLineWidth',2,'DefaultLineLineWidth',3)

set(0,'DefaultAxesFontSize',12,'DefaultAxesFontWeight','bold')

%% Generate the data set

% Time values (in seconds)

t = [1 10 10];

% Observed data (in meters)

y = m_true(1) + m_true(2)*t - m_true(3)*t.^2/2 + sigma*randn(10, 1);

% Standard deviation of the errors

sigma = 8 * ones(size(t));

% True model parameters

m_true = [10 100 9.8]; % [m1; m2; m3]

G = [ones(size(t)); t; -0.5 * t.^2];

W = diag(1./(sigma.^2));

m_ls = [G W G'] \ [G W y'];

Cov_m_ls = inv (G W G');

% Degrees of freedom

v = length(t) - length(m_ls);

% Chi-square statistic

chi_square = sum(((y - G' * m_ls) ./ sigma).^2);

p_value = 1 - chi2cdf(chi_square, v); % p-value

% Significance level

% (95% confidence interval)

alpha = 0.05;

% Z-score for alpha

z_alpha = norminv(1 - alpha/2);

confidence_intervals =

[m_ls - z_alpha sqrt(diag(Cov_m_ls)),

m_ls + z_alpha sqrt(diag(Cov_m_ls))];

fprintf('Parameter Estimates (m_ls):\n');

disp(m_ls);\

fprintf('Confidence Intervals (95%%):\n');

disp(confidence_intervals);

fprintf('Chi-Square: %.2f\n', chi_square);

fprintf('Degrees of Freedom: %d\n', v);

fprintf('p-value: %.4f\n', p_value);

t_fit = linspace(min(t), max(t), 100);

% Generate points for the fitted curve

y_fit = m_ls(1) + m_ls(2) t_fit

- (1/2) m_ls(3) * t_fit.^2;

% Fitted model

figure;

plot(t, y, 'o', 'DisplayName', 'Observed Data');

hold on;

plot(t_fit, y_fit, 'r-',

'DisplayName', 'Fitted Model');

xlabel('Time (s)');

ylabel('Distance (m)');

legend('Location', 'Best');

title('Ballistics Regression');

grid on;

Answer 1

[Image Analyst]

Tons of errors. I got tired of fixing them all, but I got this far in your script. You can continue to fix them one at a time as you go down the script:

%%
set(0,'DefaultAxesLineWidth',2,'DefaultLineLineWidth',3)
set(0,'DefaultAxesFontSize',12,'DefaultAxesFontWeight','bold')
%% Generate the data set
% Time values (in seconds)
t = [1 10 10]; 
numPoints = numel(t);
% True model parameters
m_true = [10 100 9.8]; % [m1; m2; m3]
% Standard deviation of the errors
sigma = 8 * ones(numPoints); 
% Observed data (in meters)
y = m_true(1) + m_true(2)*t - m_true(3)*t.^2/2 + sigma .* randn(1, numPoints);
G = [ones(1, numPoints); t; -0.5 * t.^2]
W = diag(1./(sigma.^2))

Answer 2

[Sam Chak]

Hi @Kathleen

Fixed "invalid expression errors" are marked by these arrows ''<--". However, the variable m_true is not provided in the code.

clear, clc, close all
%%
set(0,'DefaultAxesLineWidth',2,'DefaultLineLineWidth',3)
set(0,'DefaultAxesFontSize',12,'DefaultAxesFontWeight','bold')
%% Generate the data set
% Time values (in seconds)
t = [1 10 10]; 
% Observed data (in meters)
y = m_true(1) + m_true(2)*t - m_true(3)*t.^2/2 + sigma*randn(10, 1);

Unrecognized function or variable 'm_true'.

% Standard deviation of the errors
sigma = 8 * ones(size(t)); 
% True model parameters
m_true = [10 100 9.8]; % [m1; m2; m3]
G = [ones(size(t)); t; -0.5 * t.^2];
W = diag(1./(sigma.^2));
m_ls = [G  W  G'] \ [G  W  y'];
Cov_m_ls = inv([G  W  G']);     % <--
% Degrees of freedom
v = length(t) - length(m_ls); 
% Chi-square statistic
chi_square = sum(((y - G' * m_ls) ./ sigma).^2); 
p_value = 1 - chi2cdf(chi_square, v); % p-value
% Significance level 
% (95% confidence interval)
alpha = 0.05; 
% Z-score for alpha
z_alpha = norminv(1 - alpha/2); 
confidence_intervals = [m_ls - z_alpha  sqrt(diag(Cov_m_ls)), m_ls + z_alpha  sqrt(diag(Cov_m_ls))];    % <--
fprintf('Parameter Estimates (m_ls):\n');
disp(m_ls);     % <--
fprintf('Confidence Intervals (95%%):\n');
disp(confidence_intervals);
fprintf('Chi-Square: %.2f\n', chi_square);
fprintf('Degrees of Freedom: %d\n', v);
fprintf('p-value: %.4f\n', p_value);
t_fit = linspace(min(t), max(t), 100); 
% Generate points for the fitted curve
y_fit = m_ls(1) + m_ls(2)*t_fit - (1/2)*m_ls(3)*t_fit.^2;   % <--
% Fitted model
figure;
plot(t, y, 'o', 'DisplayName', 'Observed Data');
hold on;
plot(t_fit, y_fit, 'r-', 'DisplayName', 'Fitted Model');    % <--
xlabel('Time (s)');
ylabel('Distance (m)');
legend('Location', 'Best');
title('Ballistics Regression');
grid on;

[Image Analyst]

It's also weird that the second and third time value are the very same time of 10.