Apllying linear equation with standard error

Hi, I have a set of x,y values (triplicates) and fit a linear equation and obtain an equation with error on the slope and intersect. Until here is ok. R^2=926

I want to apply the the equation for a set of x values, but I have an error bigger than the standard errors for each x,y values, Basically MatLab is giving all these errors...But they don't make sense... I should get y= ... +- ...

Can somenone help me?

[Star Strider]

It would help to see your code, and at least a representative subset of your data.

Answer 1

[Prateekshya]

Hello Alexandre,

To apply a linear regression model to a set of x values and obtain predictions with associated errors, you need to take into account both the uncertainty in the model parameters (slope and intercept) and the variability in the data. Here is how you can achieve this in MATLAB:

Step 1: Fit a Linear Model

First, fit a linear model to your data and obtain the slope, intercept, and their standard errors.

% Example data
x = [1, 2, 3, 4, 5];
y = [2.1, 4.2, 6.1, 8.4, 10.2]; % Replace with your actual data

% Fit a linear model
mdl = fitlm(x, y);

% Get the slope, intercept, and their standard errors
slope = mdl.Coefficients.Estimate(2);
intercept = mdl.Coefficients.Estimate(1);
slopeSE = mdl.Coefficients.SE(2);
interceptSE = mdl.Coefficients.SE(1);

% Display R-squared
R2 = mdl.Rsquared.Ordinary;
fprintf('R^2 = %.3f\n', R2);

Step 2: Predict y Values and Calculate Errors

To predict y values for new x values and calculate the associated errors, you can use the predict function along with the standard errors of the coefficients.

% New x values for prediction
x_new = [6, 7, 8]; % Replace with your actual x values

% Predict y values
[y_pred, y_pred_ci] = predict(mdl, x_new');

% Display predictions with confidence intervals
for i = 1:length(x_new)
    fprintf('For x = %.2f, predicted y = %.2f, CI = [%.2f, %.2f]\n', ...
        x_new(i), y_pred(i), y_pred_ci(i, 1), y_pred_ci(i, 2));
end

Step 3: Understanding the Errors

• Standard Errors: The standard errors of the slope and intercept are used to calculate the confidence intervals for the predictions. These reflect the uncertainty in the parameter estimates.
• Prediction Intervals: The predict function provides confidence intervals for the predicted y values. These intervals account for both the uncertainty in the model parameters and the variability in the data.
• Confidence Intervals: By default, predict provides 95% confidence intervals. You can adjust this level by specifying an additional argument in the predict function.

I hope this helps!