# Thread: Problem with interpretation of regression coefficients

1. ## Problem with interpretation of regression coefficients

Hi,

I have problem with interpretation of regression coefficients. My regression function is:

y = a + b1*x + b2*x^2

How can I interpret b1 and b2 ??

Its a relationship between monetary aggregate M2 (X) and GDP (Y). There are coefficients:

y = 588,63 + 0,6312*x - 0,000005*x^2

The interpretation should be: When M2 increases by 1 mil. EUR, we can except that HDP increases by "?" mil. EUR

And my question is, what is that "?" ?

Thank you

2. ## Re: Problem with interpretation of regression coefficients

hi,
because of the second order term, you do not have a single value for the "?"
if Y= a + bx+ cx^2 then an increase of 1 unit in x will cause an increase

DY = b + 2cx +c = b+ c(2x+1) in Y.

regards

3. ## The Following User Says Thank You to rogojel For This Useful Post:

russel2000 (04-25-2015)

4. ## Re: Problem with interpretation of regression coefficients

Originally Posted by rogojel
hi,
because of the second order term, you do not have a single value for the "?"
if Y= a + bx+ cx^2 then an increase of 1 unit in x will cause an increase

DY = b + 2cx +c = b+ c(2x+1) in Y.

regards
Thank you very much! But, from where do you got "b+2cx+c" ??

Not only "b+2cx" ? From where do you got "c" addititionally?

...derivation from c*x^2 is c*2x, no c*2x+c

Or am I wrong?

5. ## Re: Problem with interpretation of regression coefficients

Well, because b1 is positive and b2 is negative implies that your (estimated) quadratic regression model indicates that as M2 increases GDP also increases - but at a diminishing rate i.e. the quadratic relationship between M2 and GDP is "concave down." Specifically, as M2 increases so does GDP - until M2 = 63119.1 and thus, GDP reaches its maximum at 20509.302. For values of M2 greater than 63119.1 than GDP decreases.

6. ## Re: Problem with interpretation of regression coefficients

I think, I understand. Thank you very much

7. ## Re: Problem with interpretation of regression coefficients

Originally Posted by russel2000
Thank you very much! But, from where do you got "b+2cx+c" ??

Not only "b+2cx" ? From where do you got "c" addititionally?

...derivation from c*x^2 is c*2x, no c*2x+c

Or am I wrong?
hi,
I calculated c(x+1)^2 -cx^2 which is c(2x+1)

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