Linear Regression Coefficient and Multiple Regression Coefficient

J

jintu7977

Guest
#1
Hello Folks:

When you use just 2 variables for regression and then when you use the same 2 variables plus an additional 2 other independent variables, for me the regression coefficient decreases for the original independent variable that I used. Is that good or bad, and normally what that does imply?

Or in more technical terms:
Now take the same dependent variable you just used. Think of two other variables from our data set that might be related to it. Put all three independent variables into a multiple regression explaining your dependent variable. Is there a change in the regression coefficient (b) on the variable that you used by itself in the previous question – can you suggest why there is or isn’t a change?

Please advice.
Thanks

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J

jintu7977

Guest
#3
I think what your asking is if the sort:

if,

y = 3 x,

and

y = 2 x + 2 z,

what does this mean?

It means that your original model was misspecified. The variables x and z are correlated and in the original model the coefficient to x is measuring a combined effect of x and z.
Look at this:
http://en.wikipedia.org/wiki/Omitted-variable_bias
Thanks for the help...

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#4
Yes, you would expect a change but try and guess ahead of time as to what that change would be so that in your minimization (guessing), you end up w/coefficients based in "reality."

When you add additional regression coefficients, the dependency on the variables "attached" to them are "alleviated" somewhat. For instance, when you go from one variable to 2, the sole dependence is lessened on the original variable and some of the dependence is transferred to the newly added variable. I think this is what you're asking?

Hello Folks:

When you use just 2 variables for regression and then when you use the same 2 variables plus an additional 2 other independent variables, for me the regression coefficient decreases for the original independent variable that I used. Is that good or bad, and normally what that does imply?

Mod Note: Please never delete an original post. All you do is remove any context from the thread and don't allow any future user to gain anything from the thread. I reverted the post back to the original. - Dason