Std Error of Regression Co-efficients.

[Pawan Punjabi]

Hi,
In regression analysis, while testing hypothesis, we are given standard error of regression co-efficient b0 & b1.
Cant logically digest, how do you find a std. Error for co-efficient. You have just 1 co-efficient number and not a set of them to take the mean and find its std error.

 

[Unemployed]

It is due to the use of inferetial statistic. Because in practice we cannot obtain all the observations of the population, we gather samples. If we can measure the whole population we would have true B0 and B1 (with capital letters). However because we use sampling, we will have b0 and b1, which we not equal to B0 and B1 but should be close with a distribution of the deviation (closer with smaller standard error, further with larger standard error),
If we repeat sampling many many many times with the same size, the samples themselve would have sampling distribution, which should be approximately normal due to the central limit theorem. Therefore, if you have b0 and b1, you should test if they are significantly different, for example, from zero. In order word, the b0 and b1 that we have could be because of the chance during the random sampling, not neccesary equal to unobserved B0 and B1.