How do I find the standard deviation of my linear regression?

I am using fitlm to do a very simple two-variable linear regression: md1 = fitlm(x,y);

Here are my results:

md1 = 

Linear regression model:
    y ~ 1 + x1

Estimated Coefficients:
                   Estimate        SE        tStat     pValue
                   ________    __________    ______    ______

      (Intercept)    0.14936      0.0022171    67.368    0     
      x1             0.98095     0.00028117    3488.8    0     

Number of observations: 278412, Error degrees of freedom: 278410
Root Mean Squared Error: 0.0203
R-squared: 0.978,  Adjusted R-Squared 0.978
F-statistic vs. constant model: 1.22e+07, p-value = 0

So what is my standard deviation?

Thanks!

Answer 1

[Star Strider]

If you want the standard deviation of the residuals (differences between the regression line and the data at each value of the independent variable), it is:

Root Mean Squared Error: 0.0203

or the square root of the mean of the squared residual values.

[Leon]

Many thanks! I didn't know RMSE is the same thing as standard deviation :-)

[Star Strider]

My pleasure!

In this instance, it is. It is the standard deviation of the residuals. The ‘usual’ definition of the standard deviation is with respect to the mean of the data. In a regression, the mean is replaced by the value of the regression at the associated value of the independent variable. The use of RMSE for a regression instead of standard deviation avoids confusion as to the reference used for the differences.

The Wikipedia article on Root-mean-square deviation goes into its usual exhaustive detail.