Re: R sq vs r sq
Good message, Jon -- :-) -- Joe - Original Message - From: Jon Cryer <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, May 05, 2000 11:13 AM Subject: Re: R sq vs r sq | But the important issue, statistically, is that the model is | linear in the _parameters_ (not the predictor variables). When this is the | case | the equations from which the least squares estimates of the parameters | are obtained are linear equations (the so-called normal equations). | This is true even when fitting a quadratic (or higher order) equation. | | Statisticians always talk about linear models in this way. Statistically | speaking, response = quadratic curve in x + random error is a _linear_ model. | Statisticians use the term nonlinear model for more complex models that are | not linear in the parameters. | | Jon Cryer | | At 07:46 PM 5/5/00 +0200, you wrote: | >Joe, | > | >Well by linear *I* meant what we mean in algebra 2 class y = mx + b, | >but I do not object to calling y = a0 + a1 x1 + a2 x2 + a3 x3 + ... linear. | >I certainly DO object to your definition of linear, although I suppose | >it *is* used by some people, I find it very confusing. | > | >Cheers, | >Bill Larson | >Geneva, Switzerland | > | >- Original Message - | >From: Joe Ward <[EMAIL PROTECTED]> | >To: William J. Larson <[EMAIL PROTECTED]>; Paul Velleman | ><[EMAIL PROTECTED]> | >Cc: <[EMAIL PROTECTED]> | >Sent: 2000 May 05 9:07 PM | >Subject: Re: R sq vs r sq | > | > | > | >Hi Paul, William et al.-- | > | >This may be ANOTHER GOOD TIME TO COMMENT ON | >THE COMMUNICATION PROBLEMS OF STATISTICS (AND OTHER AREAS, TOO). | > | >I suggest that when we use the terms LINEAR and NONLINEAR that we | >tell the reader what the SENDER means by those terms. | > | >When I write: | > | >Y = b1*X1 + b2*X2 + ... + bp*Xp + E | > | >where bi (i = 1,2,...p) are least-squares regression coefficients, I | >will refer to this as a LINEAR MODEL. | > | >The Xs can be any numbers that I choose-- log(z), ln(z), z^3, cos(z), 1/z, | >binary (1or 0), ... | > | >If a person writes the form: | > | >Y = a0 + a1*X + a2*X^2 + a3*X ^3 + E | > | >then they might say that this is a NONLINEAR model. | > | >As long as the reader knows exactly what the model is-- then we are | >communicating. | > | >In these days of fancy 3D graphic displays, it is interesting to picture the | >function: | > | >Y = a0 + a1*X + a2*X^2 | > | >in the 2D space of Y and X -- which appears as a CURVE. | > | >and then picture the function in the 3D space of Y, X and X^2 or | >re-designating X^2 as Z | > | >Y = a0 + a1*X + a2*Z | > | >We notice that the 3D function lies in a PLANE -- reminding us that | >we have a "LINEAR MODEL". | > | >If we hurriedly say to someone that "this function is NONLINEAR in the 2D | >space of Y and X, but | >LINEAR in the 3D space of Y,X and Z", then we might even cause more | >frustration. :-( | > | >"COMMUNICATION" IS A PROBLEM EVERYWHERE! | > | >DO WILLIAM AND PAUL HAVE THE SAME MEANING FOR "NONLINEAR"? | >:-) | > | >--- Joe | > | >* Joe Ward Health Careers High School * | >* 167 East Arrowhead Dr 4646 Hamilton Wolfe* | >* San Antonio, TX 78228-2402San Antonio, TX 78229 * | >* Phone: 210-433-6575 Phone: 210-617-5400* | >* Fax: 210-433-2828 Fax: 210-617-5423 * | >* [EMAIL PROTECTED]* | >* http://www.ijoa.org/joeward/wardindex.html * | > | > | > | > | > | >- Original Message - | >From: Paul Velleman <[EMAIL PROTECTED]> | >To: William J. Larson <[EMAIL PROTECTED]> | >Cc: <[EMAIL PROTECTED]> | >Sent: Friday, May 05, 2000 6:43 AM | >Subject: Re: R sq vs r sq | > | > | >| At 11:18 AM +0200 05/05/2000, William J. Larson wrote: | >| > | >| >It appears that R sq is some sort of generalization of r sq | >| >for nonlinear cases. True? | >| > | >| Not really. common convention is to capitalize the R for multiple | >| correlation. The R sqr reported in regressions allows for the | >| generalization of simple regression to a multiple regression (2 or | >| more predictors). In both cases R sqr is the squared correlation | >| between y and y-hat. Y-hat represents the best (in the least squares | >| sense) fit to y among all linear combinations of the x's. All of | >| these are
Re: R sq vs r sq
Bill -- You are so right!! The term NONLINEAR is very confusing. As I indicated in the earlier message, most folks in the statistics world refer to a LINEAR MODEL as I indicated. Y = b1*X1 + b2*X2 + ... + bp*Xp + E and some folks will write UNFORTUNATELY -- Y = b0 + b1*X1 + b2 * X2 + ... + bp*Xp + E that leads to more confusion!! The main point is that the functions are LINEAR IN THE UNKNOWN COEFFICIENTS. This is why we sometimes take the logs of the function so that the new function is LINEAR IN THE UNKNOWN COEFFICIENTS -- AND THE SOLUTIONS ARE EASIER. A "REAL" NONLINEAR MODEL NEEDS SOME SPECIAL ALGORITHMS FOR SOLUTION. --- Someday -- long after I'm out of this world -- the AP-Statistics objectives WILL ALLOW OUR STUDENTS TO HAVE -- "The power they deserve to use REGRESSION/LINEAR MODELS and COMPUTERS/CALCULATORS to their fullest". Perhaps the secondary teachers can speed up improvements through the NCTM "Principles and Standards for School Mathematics". Perhaps there should be an Applied Research Statistics course that has few restrictions on the content -- focusing on those topics that help students do what they NEED to accomplish practical results -- leading to more enthusiasm for statistics and data analysis. Change is slow!! :-) -- Joe * Joe Ward Health Careers High School * * 167 East Arrowhead Dr 4646 Hamilton Wolfe* * San Antonio, TX 78228-2402San Antonio, TX 78229 * * Phone: 210-433-6575 Phone: 210-617-5400* * Fax: 210-433-2828 Fax: 210-617-5423 * * [EMAIL PROTECTED]* * http://www.ijoa.org/joeward/wardindex.html * - Original Message - From: William J. Larson <[EMAIL PROTECTED]> To: Joe Ward <[EMAIL PROTECTED]>; Paul Velleman <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Friday, May 05, 2000 10:46 AM Subject: Re: R sq vs r sq | Joe, | | Well by linear *I* meant what we mean in algebra 2 class y = mx + b, | but I do not object to calling y = a0 + a1 x1 + a2 x2 + a3 x3 + ... linear. | I certainly DO object to your definition of linear, although I suppose | it *is* used by some people, I find it very confusing. | | Cheers, | Bill Larson | Geneva, Switzerland | | - Original Message - | From: Joe Ward <[EMAIL PROTECTED]> | To: William J. Larson <[EMAIL PROTECTED]>; Paul Velleman | <[EMAIL PROTECTED]> | Cc: <[EMAIL PROTECTED]> | Sent: 2000 May 05 9:07 PM | Subject: Re: R sq vs r sq | | | | Hi Paul, William et al.-- | | This may be ANOTHER GOOD TIME TO COMMENT ON | THE COMMUNICATION PROBLEMS OF STATISTICS (AND OTHER AREAS, TOO). | | I suggest that when we use the terms LINEAR and NONLINEAR that we | tell the reader what the SENDER means by those terms. | | When I write: | | Y = b1*X1 + b2*X2 + ... + bp*Xp + E | | where bi (i = 1,2,...p) are least-squares regression coefficients, I | will refer to this as a LINEAR MODEL. | | The Xs can be any numbers that I choose-- log(z), ln(z), z^3, cos(z), 1/z, | binary (1or 0), ... | | If a person writes the form: | | Y = a0 + a1*X + a2*X^2 + a3*X ^3 + E | | then they might say that this is a NONLINEAR model. | | As long as the reader knows exactly what the model is-- then we are | communicating. | | In these days of fancy 3D graphic displays, it is interesting to picture the | function: | | Y = a0 + a1*X + a2*X^2 | | in the 2D space of Y and X -- which appears as a CURVE. | | and then picture the function in the 3D space of Y, X and X^2 or | re-designating X^2 as Z | | Y = a0 + a1*X + a2*Z | | We notice that the 3D function lies in a PLANE -- reminding us that | we have a "LINEAR MODEL". | | If we hurriedly say to someone that "this function is NONLINEAR in the 2D | space of Y and X, but | LINEAR in the 3D space of Y,X and Z", then we might even cause more | frustration. :-( | | "COMMUNICATION" IS A PROBLEM EVERYWHERE! | | DO WILLIAM AND PAUL HAVE THE SAME MEANING FOR "NONLINEAR"? | :-) | | --- Joe | | * Joe Ward Health Careers High School * | * 167 East Arrowhead Dr 4646 Hamilton Wolfe* | * San Antonio, TX 78228-2402San Antonio, TX 78229 * | * Phone: 210-433-6575 Phone: 210-617-5400* | * Fax: 210-433-2828 Fax: 210-617-5423 * | * [EMAIL PROTECTED]* | * http://www.ijoa.org/joeward/wardindex.html * | *
Re: R sq vs r sq
Hi Paul, William et al.-- This may be ANOTHER GOOD TIME TO COMMENT ON THE COMMUNICATION PROBLEMS OF STATISTICS (AND OTHER AREAS, TOO). I suggest that when we use the terms LINEAR and NONLINEAR that we tell the reader what the SENDER means by those terms. When I write: Y = b1*X1 + b2*X2 + ... + bp*Xp + E where bi (i = 1,2,...p) are least-squares regression coefficients, I will refer to this as a LINEAR MODEL. The Xs can be any numbers that I choose-- log(z), ln(z), z^3, cos(z), 1/z, binary (1or 0), ... If a person writes the form: Y = a0 + a1*X + a2*X^2 + a3*X ^3 + E then they might say that this is a NONLINEAR model. As long as the reader knows exactly what the model is-- then we are communicating. In these days of fancy 3D graphic displays, it is interesting to picture the function: Y = a0 + a1*X + a2*X^2 in the 2D space of Y and X -- which appears as a CURVE. and then picture the function in the 3D space of Y, X and X^2 or re-designating X^2 as Z Y = a0 + a1*X + a2*Z We notice that the 3D function lies in a PLANE -- reminding us that we have a "LINEAR MODEL". If we hurriedly say to someone that "this function is NONLINEAR in the 2D space of Y and X, but LINEAR in the 3D space of Y,X and Z", then we might even cause more frustration. :-( "COMMUNICATION" IS A PROBLEM EVERYWHERE! DO WILLIAM AND PAUL HAVE THE SAME MEANING FOR "NONLINEAR"? :-) --- Joe * Joe Ward Health Careers High School * * 167 East Arrowhead Dr 4646 Hamilton Wolfe* * San Antonio, TX 78228-2402San Antonio, TX 78229 * * Phone: 210-433-6575 Phone: 210-617-5400* * Fax: 210-433-2828 Fax: 210-617-5423 * * [EMAIL PROTECTED]* * http://www.ijoa.org/joeward/wardindex.html * - Original Message - From: Paul Velleman <[EMAIL PROTECTED]> To: William J. Larson <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Friday, May 05, 2000 6:43 AM Subject: Re: R sq vs r sq | At 11:18 AM +0200 05/05/2000, William J. Larson wrote: | > | >It appears that R sq is some sort of generalization of r sq | >for nonlinear cases. True? | > | Not really. common convention is to capitalize the R for multiple | correlation. The R sqr reported in regressions allows for the | generalization of simple regression to a multiple regression (2 or | more predictors). In both cases R sqr is the squared correlation | between y and y-hat. Y-hat represents the best (in the least squares | sense) fit to y among all linear combinations of the x's. All of | these are statistics for linear models. It is dangerous to apply them | to nonlinear models. | | -- Paul | -- | Paul F. Velleman | Cornell University Data Description, Inc. | 358 Ives Hall Box 4555 | Ithaca, NY 14853 Ithaca, NY 14852-4555 | (607) 255-4411 (607) 257-1000 | (607) 255-8484 fax(607) 257-4146 fax | === | The Advanced Placement Statistics List | To UNSUBSCRIBE send a message to [EMAIL PROTECTED] containing: | unsubscribe apstat-l | Discussion archives are at | http://forum.swarthmore.edu/epigone/apstat-l | Problems with the list or your subscription? mailto:[EMAIL PROTECTED] | === | === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
