I have a qns, let say an original Regesssion to is be estimated as follows:
Y = B + b1x1 + b2x2 Then, if diagnostic test suggests that the relationship between Y and x1 is nonlinear, add a variable X3 (which is square of X1). Y = B + b1x1 + b2x2 + b3(x1*x1) Qns: how to interpret X1 since it has both a linear and nonlinear relationship Post a follow-up to this message Message 2 in thread From: Don Libby ([EMAIL PROTECTED]) Subject: Re: Weird instruction found in an econ text View this article only Newsgroups: sci.econ Date: 2004-02-21 02:52:07 PST "chokie" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > I have a qns, let say an original Regesssion to is be estimated as > follows: > > Y = B + b1x1 + b2x2 > > Then, if diagnostic test suggests that the relationship between Y and > x1 is nonlinear, add a variable X3 (which is square of X1). > > Y = B + b1x1 + b2x2 + b3(x1*x1) > > > Qns: how to interpret X1 since it has both a linear and nonlinear > relationship Relationship between Y and X is quadradic: this is the first term of the Taylor Series appoximation to the exponential function, which sometimes gives a not-too-bad approximation to the relationship Y = e^X, which means Y accelerates (or decelerates) as X increases. -dl Post a follow-up to this message Message 3 in thread From: Robert Vienneau ([EMAIL PROTECTED]) Subject: Re: Weird instruction found in an econ text View this article only Newsgroups: sci.econ Date: 2004-02-21 13:30:10 PST In article <[EMAIL PROTECTED]>, "Don Libby" <[EMAIL PROTECTED]> wrote: > "chokie" <[EMAIL PROTECTED]> wrote in message > news:[EMAIL PROTECTED] > > Then, if diagnostic test suggests that the relationship between Y and > > x1 is nonlinear, add a variable X3 (which is square of X1). > > > > Y = B + b1x1 + b2x2 + b3(x1*x1) > > > > > > Qns: how to interpret X1 since it has both a linear and nonlinear > > relationship > Relationship between Y and X is quadradic: this is the first term of the > Taylor Series appoximation to the exponential function, which sometimes > gives a not-too-bad approximation to the relationship Y = e^X, which > means Y > accelerates (or decelerates) as X increases. The Taylor series for exp( x ) is 1 + x +x^2/2 + ... + x^n/n + ... It seems confused to describe the linear regression relationship between Y and X above as the first term of the Taylor series approximation to the exponential function, since, in most cases the coefficients will not have desired ratios to one another. -- Try http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Bukharin.html To solve Linear Programs: .../LPSolver.html r c A game: .../Keynes.html v s a Whether strength of body or of mind, or wisdom, or i m p virtue, are found in proportion to the power or wealth e a e of a man is a question fit perhaps to be discussed by n e . slaves in the hearing of their masters, but highly @ r c m unbecoming to reasonable and free men in search of d o the truth. -- Rousseau Post a follow-up to this message Message 4 in thread From: Robert Vienneau ([EMAIL PROTECTED]) Subject: Re: Weird instruction found in an econ text View this article only Newsgroups: sci.econ Date: 2004-02-21 16:08:07 PST > "chokie" <[EMAIL PROTECTED]> wrote in message > news:[EMAIL PROTECTED] > > I have a qns, let say an original Regesssion to is be estimated as > > follows: > > > > Y = B + b1x1 + b2x2 > > > > Then, if diagnostic test suggests that the relationship between Y and > > x1 is nonlinear, add a variable X3 (which is square of X1). > > > > Y = B + b1x1 + b2x2 + b3(x1*x1) > > > > > > Qns: how to interpret X1 since it has both a linear and nonlinear > > relationship? I don't find any problem of interpretation above. But perhaps the following will help: Y = B + b1x1 + b2x2 + b3(x1*x1) is equivalent to Y = [ B - b2 b2/(4 b3) ] + b1 x1 + b3 x4 x4 where x4 = x1 + b2/(2 b3 ) That is, Y is linear in x1 and the square of x4. -- Try http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Bukharin.html To solve Linear Programs: .../LPSolver.html r c A game: .../Keynes.html v s a Whether strength of body or of mind, or wisdom, or i m p virtue, are found in proportion to the power or wealth e a e of a man is a question fit perhaps to be discussed by n e . slaves in the hearing of their masters, but highly @ r c m unbecoming to reasonable and free men in search of d o the truth. -- Rousseau Post a follow-up to this message Message 5 in thread From: chokie ([EMAIL PROTECTED]) Subject: Re: Weird instruction found in an econ text View this article only Newsgroups: sci.econ Date: 2004-02-22 08:01:46 PST Robert Vienneau <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > > "chokie" <[EMAIL PROTECTED]> wrote in message > > news:[EMAIL PROTECTED] > > > I have a qns, let say an original Regesssion to is be estimated as > > > follows: > > > > > > Y = B + b1x1 + b2x2 > > > > > > Then, if diagnostic test suggests that the relationship between Y and > > > x1 is nonlinear, add a variable X3 (which is square of X1). > > > > > > Y = B + b1x1 + b2x2 + b3(x1*x1) > > > > > > > > > Qns: how to interpret X1 since it has both a linear and nonlinear > > > relationship? > > I don't find any problem of interpretation above. But perhaps the > following will help: > > Y = B + b1x1 + b2x2 + b3(x1*x1) > > is equivalent to > > Y = [ B - b2 b2/(4 b3) ] + b1 x1 + b3 x4 x4 > > where > > x4 = x1 + b2/(2 b3 ) > > That is, Y is linear in x1 and the square of x4. > > -- Maybe I should frame this in context. Suppose the dependent variable is career prospects and X1 refers to the level of education. In such an equation, am I saying that career prospects are both positively (linear) associated with the level of education and also curvilinearly associated with the level of education. In terms of econometric interpretation, I would not know how to interpret X4. I do notice that x4 is additive, incuding the beta of x2. Now, let say that X2 refers to a totally unrelated variable such as race or location. How would you interpret the relationship? Post a follow-up to this message Message 6 in thread From: Robert Vienneau ([EMAIL PROTECTED]) Subject: Re: Weird instruction found in an econ text View this article only Newsgroups: sci.econ Date: 2004-02-22 09:12:09 PST In article <[EMAIL PROTECTED]>, Robert Vienneau <[EMAIL PROTECTED]> wrote: > > "chokie" <[EMAIL PROTECTED]> wrote in message > > news:[EMAIL PROTECTED] > > > I have a qns, let say an original Regesssion to is be estimated as > > > follows: > > > > > > Y = B + b1x1 + b2x2 > > > > > > Then, if diagnostic test suggests that the relationship between Y and > > > x1 is nonlinear, add a variable X3 (which is square of X1). > > > > > > Y = B + b1x1 + b2x2 + b3(x1*x1) > > > > > > > > > Qns: how to interpret X1 since it has both a linear and nonlinear > > > relationship? > I don't find any problem of interpretation above. But perhaps the > following will help: > > Y = B + b1x1 + b2x2 + b3(x1*x1) > > is equivalent to > > Y = [ B - b2 b2/(4 b3) ] + b1 x1 + b3 x4 x4 > > where > > x4 = x1 + b2/(2 b3 ) > > That is, Y is linear in x1 and the square of x4. Whoops. I should have written: Y = [ B - b1 b1/(4 b3) ] + b2 x2 + b3 x4 x4 where x4 = x1 + b1/(2 b3 ) I think these questions are appropriately cross-posted, at least, to, say, sci.stat.edu. -- Try http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Bukharin.html To solve Linear Programs: .../LPSolver.html r c A game: .../Keynes.html v s a Whether strength of body or of mind, or wisdom, or i m p virtue, are found in proportion to the power or wealth e a e of a man is a question fit perhaps to be discussed by n e . slaves in the hearing of their masters, but highly @ r c m unbecoming to reasonable and free men in search of d o the truth. -- Rousseau Post a follow-up to this message . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
