Regression error data

Hi after plotting the regression line and inserting the error I have noticed that it doesn't seem to have an error on it i.e. I want the equation to be in:

y = ax±b + c±d

format rather than

y = ax±c

I would also like to display the rsquare value of the fit. How would I be able to do this?

Thank you in advance

Answer 1

[Wayne King]

Let

y = a(:,2);
x1 = a(:,1);

I'm assuming the 2nd column is the dependent variable and the first column is your predictor, independent variable.

Then,

   X = [ones(size(x1)) x1];
   [b,bint,r,rint,stats] = regress(y,X);
   rsquared = stats(1) % this is the R-squared
   % plot the data and the fit
   yhat = b(1)+b(2)*x1;
   plot(x1,y,'b*');
   plot(x1,yhat,'r-.');

[Suguru]

Hi thanks for your help! :)

Managed to plot the line and get the regression coefficient.

One last thing how do I output the equation of the line with errors?

Many thanks

[Wayne King]

The errors are the residuals. But just so you understand, the errors here are y-yhat, the actual data values- fitted value.

[Suguru]

Ah I see what you mean thank you problem solved now :)

Answer 2

[Wayne King]

Hi, the simple linear regression model is

y = beta0 + beta1*x+epsilon

where epsilon is the error.

But when you fit the model, you only fit the beta0 (intercept) and beta1 (slope) terms, so you fit a model of the form

yhat = \hat{beta0}+\hat{beta1}*x

I've used \hat{} to designate estimates.

You can output the rsquared value as below.

load carsmall
x1 = Weight;
y = MPG;
X = [ones(size(x1)) x1];
[b,bint,r,rint,stats] = regress(y,X);
rsquared = stats(1)

The fitted model is:

    yhat = b(1)+b(2)*x1;
    plot(x1,y,'b*');
    plot(x1,yhat,'r-.');

The errors, residuals, are in the r variable.

[Suguru]

Sorry still a bit confused on the fit so let's say I have a 10rowx2column variable a and plotted a scatter by:

scatter(a(:,1),a(:,2))

What commands would I use to plot a fit in the format that you have told me? (I've used the GUI to the the initial fit so I don't quite know the command for it... I did google but its not very clear...)