Standard error of estimates - Linear Regression

Hi, the question gives the following data:

x | 1.2 | 1.0 | 1.5 | 1.2 | 1.4 |

Y | 25 | 40 | 10 | 27 | 16 |

I worked out the estimated regression function and got Y=97.21-58.42x

(using Y=b1+b2x,

b2=Sxy/Sxx=-8.88/0.152=-58.42

b1=Ybar-b2xbar=23.6-(-58.42*1.26)=97.21)

So at this stage I need to work out the standard error of both b1 and b2, which are the square roots of the estimated variances for b1 and b2. Is there a formula for this part? I'm guessing there is, just struggling to find it in an understandable form!

Thanks

Re: Standard error of estimates - Linear Regression

Hey Mick.

There are standard formulas for this and they are Var(B0_hat) = sigma^2(1/n + 1/SXX) and Var(B1_hat) = sigma^2/SXX and you can estimate sigma^2 with sigma_hat^2 which is given by sigma_hat^2 = [SYY - B1_hat^2*SXX]/(n-2).

I'm not sure what you have to do in your course, but these are some standard identities for a simple linear regression. For a multiple linear regression you can estimate the covariance matrix and use that to get all the information.

Re: Standard error of estimates - Linear Regression

Thanks, I had the formulas for Var(B0_hat) and Var(B1_hat), just for some reason had forgotten what to do about sigma^2.

Anyway from there onwards it's just plugging the numbers into the equations so thanks :)