Question

I have data and I need to do a linear regression on the data to obtain

y=Alpha*x+Beta

Alpha and Beta are estimators given by the regression, polyfit can give me those with no problem but this is a physical science report and I need to give error estimators on those values

I know from statistics that standard deviation exists for simple linear regression coefficients.

How can I calculate then in Matlab

Thank you

Answer 1

The second output of the regress command will give you 95% confidence intervals for the regression coefficients. Here’s an example:

>> x = [ones(100,1), (1:100)'];
>> alpha = 3; beta = 2;
>> y = x*[alpha; beta]+randn(100,1);
>> [coeffs, coeffints] = regress(y,x);
>> coeffs
coeffs =
       2.9712
       1.9998
>> coeffints
coeffints =
       2.5851       3.3573
       1.9932       2.0064

Here alpha has been estimated 2.9712, with 95% confidence interval of between 2.5851 and 3.3573, and beta has been estimated as 1.9998, with 95% confidence interval between 1.9932 and 2.0064.