Std. Error Multiple Regression Question

[sumie]

Hi guys,

I'm stuck at interpreting the stadard error. In single regression it's clear, it's just the average distance from the line. But I don't really understand what this looks like in multiple regression. Does the standart error depend on the estimate or do I have to look at it in an absolute way? E.g. if my estimate is bigger, is my standart error going to be bigger automatically? Or are they independent?

Thanks in advance.

Edit: A link which I found very helpful in answering this question is:

http://support.minitab.com/en-us/mi...hat-is-the-standard-error-of-the-coefficient/

 

[sumie]

--------------

 

[GretaGarbo]

When you estimate something, in a model like this:

y = a + b1*x1 + b2*x2 + eps


then the standard deviation in eps will say how big the "spread" is in the swarm of points (in a simple regression model and in a multiple regression model). This standard deviation is usually called sigma. The estimated standard deviation will be about the same even if the sample size is small or large.

However, the standard error is different. That is why I don't agree with the this statement:

However, i'm stuck at interpreting the stadard error. In single regression it's clear, it's just the average distance from the line.

The standard error expresses the "uncertainty" in the estimated parameters (the values under "Estimate" in the printout.) As the sample size increases the standard error will be lower. (Of course with ten thousand or ten millions observations the parameter estimates would be more precise.)

You look at the parameter estimate and compared that with the standard error. The ratio: "Estimate"/standard error will give the t-value. The t-value need to be larger than two (in absolute value) to be statistically significant.

- - -

Hmm!

It seems like while I was writing an answer (and been interrupted by other things) the original poster "sumie" deleted all the content of his post. That makes my answer essentially meaningless. It does not feel very rewarding to answer.

Sumie! The idea with this site is that many can ask, many can answer, and many can read and learn. Your action make it impossible for other readers to gain. If you want private consulting, go to a consulting company and pay the fee!

 

[sumie]

@GretaGarbo
I'm very sorry. I thought that no-one was going to answer the question, resp I did not know you were writing the answer. I just wanted to show that no-one should have to answer this question as I learned the answer via another way. I will try to reconstruct the question so others can gain.

 

[rogojel]

hi,
describe the answer as well, that would be even better.