linearity

how to know that the graphical plot is linear till what extend? and i need to program for the same with the matlab command

[Walter Roberson]

All plots are linear to within some error measure. You need to be clearer about your goals.

Answer 1

[Divyam]

Hi @puneeth kumar.s,

Considering that you are plotting data and trying to determine linearity based on how well the data fits a linear model. Calculating the value for the data and a linear model can help you determine the extent of its linearity.

% Using sample data for x and y 
x = linspace(0, 10, 100); % Independent variable
y = 2 * x + 3 + randn(size(x)); % Linear relationship with some noise

% Fit a linear model
p = polyfit(x, y, 1); 
y_fit = polyval(p, x);

% Calculate R^2
SS_res = sum((y - y_fit).^2); % Residual sum of squares
SS_tot = sum((y - mean(y)).^2); % Total sum of squares
R_squared = 1 - (SS_res / SS_tot);

% Display R^2 value
fprintf('The coefficient of determination (R^2) is: %.2f\n', R_squared);

% Determine extent of linearity
threshold = 0.95; 
if R_squared >= threshold
    fprintf('The plot is linear to a high degree (R^2 >= %.2f).\n', threshold);
else
    fprintf('The plot is not linear to a high degree (R^2 < %.2f).\n', threshold);
end

Note: an value close to 1 determines a strong linear relationship.

For more information regarding the value, you can refer to the theoretical section of this documentation: https://www.mathworks.com/help/stats/coefficient-of-determination-r-squared.html