Posted on Wednesday, 21st March 2012

Please read secs 12.5.1-12.5.3 and post a comment.

Posted in Class | Comments (15)

  1. Eric VanEpps Says:
    March 21st, 2012 at 4:35 pm

    In equation 12.60, you show that the variance matrix R can be used, but I’m still not clear on what exactly R is. What does it refer to and how would it be found in a typical multiple regression problem?

  2. Sharlene Flesher Says:
    March 21st, 2012 at 7:32 pm

    The examples were very helpful, especially with interpreting the t ratios, but I’m not sure I fully understand how to interpret them. Could you elaborate on this, and the V subspace concept of Figure 12.7?

  3. Rob Rasmussen Says:
    March 21st, 2012 at 8:17 pm

    I am having trouble understanding how the F-ratio is interpreted for the case of multiple linear regression (ex 12.5 and table 12.2).

  4. Rich Truncellito Says:
    March 21st, 2012 at 9:11 pm

    Could there ever be an instance in which adding a predictive variable to a multiple regression model worsens the fit, as measured by R^2?

  5. Jay Scott Says:
    March 21st, 2012 at 10:56 pm

    Can you discuss figure 12.7 on p.385? It is difficult to see what vectors are being added or how projections are being made from the vectors. I am unclear how this relates to the matrices on the previous pages.

  6. Shubham Debnath Says:
    March 21st, 2012 at 11:56 pm

    When using matrices for multiple regression, is it helpful to reduce a matrix to upper echelon or echelon form? And how can one apply nonlinear regression models similarly?

  7. Ben Dichter Says:
    March 22nd, 2012 at 12:37 am

    Is linear regression always performed assuming normal error? Are there instances when you would use a different error estimate and would you be able to find a closed form solution?

  8. Ben Dichter Says:
    March 22nd, 2012 at 12:38 am

    Is linear regression always performed assuming normal noise? Are there instances when you would use a different noise model and would you be able to find a closed form solution? Would you be able to perform an analogous ANOVA?

  9. Rex Tien Says:
    March 22nd, 2012 at 12:38 am

    I am still not quite sure how to calculate the sigma^2 and s^2 in equation 12.56. Which x-values does it arise from?

    Also, I appreciated the geometric argument in helping understand the matrix form of the least-squares fit. However, why does this insight apply to least squares and not other methods like least-absolute value?

  10. Matt Panico Says:
    March 22nd, 2012 at 3:07 am

    When bootstrapping multivariate regressions, the bootstrapped sample sets will almost always generate a better fit (and smaller residuals) than the original data, due to repeated data. Does this cause an issue with analysis?

  11. Yijuan Du Says:
    March 22nd, 2012 at 7:33 am

    How to represent the interaction of these explanatory variables?

  12. David Zhou Says:
    March 22nd, 2012 at 7:40 am

    Does the least squares fit principle basically say that if you have over constraining variables, you’re never going to find a linear combination of them to exact regress to a line, so you project to as many dimensions as you can? I think I’m familiar with the linear algebra behind it, but can you go over the statistical principles involved?

    (This is one section ahead I realize.) How do you use polynomial and cosine regression? Do you have to assume that some model fits ad hoc? Is there any way to compute the order of the polynomials, or is it something you just fit and compare? I guess this goes back to what you say – all models are wrong, but some are useful?

  13. Amanda Markey Says:
    March 22nd, 2012 at 7:42 am

    We talked about corrections for multiple hypothesis tests yesterday. Is there a penalty for generating many multiple regressions (each time changing which x’s are included)?

  14. Noah Says:
    March 22nd, 2012 at 8:05 am

    When the F-statistic does not follow a F-distribution, is it completely useless? Or, can a different distribution be fit to the available F-statistics in order to make conclusions about the data? I would assume this would require being able to generate a large number of F-statistics (like in the HW), is that correct?

  15. Thomas Kraynak Says:
    March 22nd, 2012 at 8:30 am

    The procedures seem pretty straightforward when it comes to performing multiple regression using two, three, or four explanatory variables as related to doing a simple linear regression with one variable. Are there issues associated with using more variables than that? What is the “limit” of number of multiple regression variables typically used in the literature?

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