Quantitative Methods (Std. Error)

[travelin.man119]

Sometimes standard error is defined as the coefficient/t-stat. Sometimes all the info is given almost in chart form including coefficient, standard error, and t-stat but the standard error does not equal the coefficient/t stat like it should. is there more than one standard error like one is for each independent variable (coefficient) and another is for the equation as a whole? can someone please help

 

[dwheats]

By definition:
standard error = (standard deviation)/sqrt
But if the t-stat was computed on a hyopothesis test to see if the coefficient is equal to zero, we can also solve for the standard error:
t=(Xbar - mu)/(std err)
Then we are looking to see that mu=0, so
t = Xbar/(std err)
and it follows that
std err = Xbar / t

 

[S2000magician]

Clarifying further:
In an Anova table the output from a regression analysis, the statistical tests on the regression parameters (slopes and intercept) are computed assuming that the hypothesized values are all zero. Because of this, you can use the derivation dwheats gave to explain the t-value. Note that if you want to test whether a particular parameter is equal to something other than zero, the numbers in the table are incorrect; you have to calculate your own t-statistics.

 

[CMLSML]

^ where does t-stat come into play in an Anova table???? If you are being loosey goosey and generally referring to regression output - that would make sense.

 

[S2000magician]

CMLSML wrote:^ where does t-stat come into play in an Anova table???? If you are being loosey goosey and generally referring to regression output - that would make sense.

Yes, I am.
I might say that I’d replied in the midst of a bunch of other things going on around me and was quite distracted, but that’s no excuse.
I’ve corrected the egregious error.

 

[tickersu]

travelin.man119 wrote:
Sometimes standard error is defined as the coefficient/t-stat.

This relationship only holds for the standard error of the specific coefficient estimate.

travelin.man119 wrote:
is there more than one standard error like one is for each independent variable (coefficient) and another is for the equation as a whole?

There is a standard error for each estimated coefficient, and there is a standard error of the regression (SER), which is also sometimes called the standard error of the estimate (SEE).