Standard Error

[sumeetg]

We regressed weekly Lotto expenditures, Y(i), against weekly disposable income, X(i) to generate the following sample regression function (SRF): Y(i) = 1.527 + 0.106*X(i). The standard error of regression (SER) is 2.0327. The variance of X(i) is 5,156.3. The sample size is 10 (n=10). What is the standard error of the slope coefficient, se(b2)?
a) 0.001
b) 0.003
c) 0.009
d) 0.027

Can someone please help me with this?

 

[afterworkguinness]

Hi Sumeetg,
Stand error of the slope is given by sqrt[(standard error of the regression^2)/(variance of x)*n-1)] which gives a result of c.

you can break this formula down a bit:

sqrt[ (residual sum of squares/n-k-1 )^2 / SUM(X(i) - Xbar)^2]

standard error of the regression^2 = (residual sum of squares/n-k-1 )^2

As we know, sample variance of X(i) = SUM [(X(i)-Xbar)^2]/n-1
Thus to get SUM(X(i) - Xbar)^2 in the denominator we take the sample variance and multiple by n-1

Hope that helps.

 

[David Harper CFA FRM]

fyi source is here (paid members only) as 89.2: http://forum.bionicturtle.com/threads/l1-t2-89-ols-standard-errors.3861