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Math Help - Standard error of estimates - Linear Regression

  1. #1
    Junior Member
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    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
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  2. #2
    MHF Contributor
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    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.
    Thanks from Mick
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  3. #3
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    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
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