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Re: comparing two betas
Ambiguous question. By "beta" do you mean (as some would) a standardized regression coefficient? Or do you mean (as some would, perhaps especially in the context of testing hypotheses) the population value of a raw regression coefficient? Further, you specify "multiple regression equations", not "simple regression", which implies that each equation has several betas. Did you wish to compare only one of them, between the two equations, or several of them, or the whole vector of betas? By "Both equations have the same configuration" I understand you to mean that they express the same model (same response variable, same predictors), on two different data sets (else there would not be two equations). How are the two data sets related? If each is independent of the other, that's one thing; but if (e.g.) the regression model is fitted to the data of wives in the one instance and to their husbands in the other, that's another thing entirely. On Mon, 9 Oct 2000, rjkim wrote: I am looking for a formula that does the comparison between two betas (from two multiple regression equations). Both the equations have the same configuration. And I want to conduct a significant test for the difference between the betas. Any hint will be greatly appreciated. Do you really mean "a formula", or are you asking for a procedure that mith be implemented in a statistical computing package? -- Donald F. Burrill[EMAIL PROTECTED] 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED] MSC #29, Plymouth, NH 03264 (603) 535-2597 Department of Mathematics, Boston University[EMAIL PROTECTED] 111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288 184 Nashua Road, Bedford, NH 03110 (603) 471-7128 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: comparing two betas
Let me quote from my own old message sent to sci.stat.math: The appropriate method is given by using dummy (0 / 1) variables in regression. If added constructed variables are not significant then coefficients are the same (statistically). If you test for *all* coefficients then this method will give you Chow test. Some references: Pagan, A.R., and D.F.Nicholls. "Estimating Predictions, Prediction Errors and Their Standard Deviations Using Constructed Variables," Journal of Econometrics, 24 (1984), 293-310. Chow, G.C. "Tests of Equality between Sets of Coefficients in Two Linear Regressions," Econometrica, 28 (1960), 591-605. A. Tsyplakov Novosibirsk State University rjkim [EMAIL PROTECTED] wrote in message 8rsema$56s$[EMAIL PROTECTED]">news:8rsema$56s$[EMAIL PROTECTED]... Hello, I am looking for a formula that does the comparison between two betas (from two multiple regression equations). Both the equations have the same configuration. And I want to conduct a significant test for the difference between the betas. Any hint will be greatly appreciated. Thanks in advance. June Rhee = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Memorizing Formuas
Who is in the class? What is your audience? Non math-inclined? Education major? Business major? Statistics Major? Math Major? Social-Science Major? The approach should be different for each group. The understandings learned by all should be the same but the math work should be modified so that it doesn't "scare off" certain groups. If you stress the math, you will lost many individuals who should be using statistical analysis and its principles in their future careers. Take a look at how many individuals "fall on their face" when the unit on probability is taught. If you go into too much detail in that unit you can easily turn off students. I always worried about the student who needed the statistical concepts but got bogged down in the unit on probability. Look at some of the questions at the end of that chapter. Are they really important and or/practical? I taught for many years and always had my students prepare 5"x7" or 6"x8" cards with sample problems on one side and a worked out problem on the reverse side. Assuming that when a student leaves the university level they may not be using statistical analysis in their everyday work, I wanted them to be able to refresh their knowledge of statistics quickly and easily when they had to do random statistical analysis of data, such as to check reports of another person or check information given in magazines or journals. I also assumed that if the student was going to make their life work statistical analysis, they would be involved everyday and would, in all probability, be using statistical software (SAS, SPSS, Modstat, Excel, or some other commercial product) and would be more involved in setting up/and or running the analysis. At that point in time I didn't think they would need to have memorized all the formulas. My concern was for the non-statistical analysis professional. I wanted them to have a handy, useful reference. The cards seemed the best way to go. During tests, I allowed students to use their reference cards. They seemed more comfortable while working out the problems on the tests. I made sure that there were enough test questions to assure me that the student had a good understanding of the statistical approach to each analysis. In later years I allowed students to use their PC in class, and supplied school PC's for the students during test taking time. My concern was that the student knew how to approach the analysis, how to decide on the proper test, knew the restrictions of that test, knew how to interpret the results of the test and then how to deteremine if the proposed hypotheses were either accepted or rejected. The math work is the "grunt" work and I felt it should take a back-seat to the understanding of the work to be done. Just my two-cents. Dr. Robert C. Knodt 4949 Samish Way, #31 Bellingham, WA 98226 [EMAIL PROTECTED] "Everyone has a photographic memory. Some just don't have film." = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: memorizing formulas
- Forwarded message from Michael Granaas - I honestly believe that there is something to be learned from memorizing several of the basic formulas that are involved in defining statistics. I, less elegantly, tell my students that it is important to have this basic understanding so that it can 1) be utilized when we have the machines start doing the computations for us and 2)be drawn on for understanding when the mathematics is no longer so simple. - End of forwarded message from Michael Granaas - I doubt your students will gain ANY understanding from memorizing formulae. Once they have the understanding, then formulae MIGHT provide a summary or reminder -- but only for students who are VERY fluent at READING mathematics -- as opposed to mindlessly manipulating formulae. I do not see any such students in the undergraduate introductory course that I often teach. I noted that Karl presented all the understandings he sought verbally on the list. Why not do the same in class? _ | |Robert W. Hayden | | Work: Department of Mathematics / |Plymouth State College MSC#29 | |Plymouth, New Hampshire 03264 USA | * |fax (603) 535-2943 /| Home: 82 River Street (use this in the summer) | )Ashland, NH 03217 L_/(603) 968-9914 (use this year-round) Map of New[EMAIL PROTECTED] (works year-round) Hampshire http://mathpc04.plymouth.edu (works year-round) The State of New Hampshire takes no responsibility for what this map looks like if you are not using a fixed-width font such as Courier. "Opportunity is missed by most people because it is dressed in overalls and looks like work." --Thomas Edison = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: memorizing formulas
I think that Bob Hayden is on to something essential here ("I noted that
Karl presented all the understandings he sought verbally on the list. Why
not do the same in class?"). I think of the "definitional formulae" just as
a convenient shorthand for the verbal definition of a construct. But it may
be the case that most of our students assume that something that looks like
a formula is just for use with mindless computations. They may have learned
this in their first 12 years of schooling, where formulas may indeed be
presented as nothing more than mindless recipes for getting some quantity
not really well understood. How can we break our students of that bad
habit? I do frequently verbalize the 'formula' after writing it on the
board -- for variance, saying something like "look at this, we just take the
sum of the squared deviations of scores from their mean, which measures how
much the scores differ from one another, and then divide that sum by N, to
get a measure of how much scores differ from one another, on average." The
shorthand is really convenient, I don't know how I would get along without
it.
I have always thought that success in stats courses was much more a
function of a student's verbal aptitude and ability to think analytically,
rather than mathematical aptitude. Has anybody actually tested this
hypothesis?
- Forwarded message from Michael Granaas -
I honestly believe that there is something to be learned from
memorizing several of the basic formulas that are involved in defining
statistics. I, less elegantly, tell my students that it is important
to have this basic understanding so that it can 1) be utilized when we
have the machines start doing the computations for us and 2)be drawn
on for understanding when the mathematics is no longer so simple.
- End of forwarded message from Michael Granaas -
I doubt your students will gain ANY understanding from memorizing
formulae. Once they have the understanding, then formulae MIGHT
provide a summary or reminder -- but only for students who are VERY
fluent at READING mathematics -- as opposed to mindlessly manipulating
formulae. I do not see any such students in the undergraduate
introductory course that I often teach. I noted that Karl presented
all the understandings he sought verbally on the list. Why not do the
same in class?
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Re: memorizing formulas
"Karl L. Wuensch" wrote: I have always thought that success in stats courses was much more a function of a student's verbal aptitude and ability to think analytically, rather than mathematical aptitude. Has anybody actually tested this hypothesis? 1. This clearly depends on the particular (type of) stats course. 2. I would find 'ability to think analytically' hard to distinguish from 'mathematical aptitude' - although I accept that some narrow definitions of both characteristics may have minimal overlap. Alan -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102Fax: +61 03 9903 2007 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Random Walk
In a random walk with state space = Z and transition probabilities P(k -- k+1)=p, P(k -- k)=r, P( k -- k-1)=q with p+q+r=1, the expected number of steps before moving up is either finite or infinite depending on p, q, r. This means (applied to the stock market) that it is possible for a stock price to never surpass its present value. I am looking for a proof that someone with NO mathematical background could understand. Tthe easiest proof I have so far requires knowledge of recurrence relations and basic arithmetic (+, -, *, /). I would like to put this proof on my financial web site. The author of the proof would be acknowledged. Thank you. Vincent Granville -- http://www.datashaping.com : Advanced Trading Strategies = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
