Rachev Chapters 2 & 3
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Hi skoh, see the source, where I happened to have previously elaborated on that: http://forum.bionicturtle.com/threads/l1-t2-112-rachevs-properties-of-normal-distribution.3979/
Thanks,
Thanks,
Hi skoh,
OLS regression coefficients are sample means (averages) which in practice (since we don't know the population variance) are characterized by a student's t distribution. If we just take the mean of a sample--e.g., sample mean of {1,2,3,4,5} = 3--that sample mean has only one (1) degree of freedom. Such that it has df = n-1 = 5-1 = 4.
But the multivariate regression "The regression produces four regression coefficients, an intercept plus three partial slope coefficients." computes 4 sample means, one for each coefficient (some will write that df = number of variables, which is true, since the regression has 3 independents + 1 dependent, but's it really the 4 coefficients: 3 slopes + 1 intercept). So, it's a "more sophisticated" mean that is produced by an OLS regression. So, here the df for the t-ratio variable = n - 4 = 32 - 4 = 28. (then the variance of df/[df-2] is just property of the student's t). I hope that explains, thanks,
OLS regression coefficients are sample means (averages) which in practice (since we don't know the population variance) are characterized by a student's t distribution. If we just take the mean of a sample--e.g., sample mean of {1,2,3,4,5} = 3--that sample mean has only one (1) degree of freedom. Such that it has df = n-1 = 5-1 = 4.
But the multivariate regression "The regression produces four regression coefficients, an intercept plus three partial slope coefficients." computes 4 sample means, one for each coefficient (some will write that df = number of variables, which is true, since the regression has 3 independents + 1 dependent, but's it really the 4 coefficients: 3 slopes + 1 intercept). So, it's a "more sophisticated" mean that is produced by an OLS regression. So, here the df for the t-ratio variable = n - 4 = 32 - 4 = 28. (then the variance of df/[df-2] is just property of the student's t). I hope that explains, thanks,
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