{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Q3 - But if we add a variable whose t-statistic is less...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
the Akaike Information Criterion (AIC) R Squared and Adjusted R Squared The R Squared is R2 = 1 – ESS / TSS. It is 1 if and only if ESS = 0, i.e. there are no errors… y = yhat… the fit is exact at every data point. In addition, there is a crucial fact pertaining to the use of R Squared as a measure of improvement: if we add a variable to a regession, the R Squared cannot decrease. It doesn’t have to go up, but it cannot get smaller. In other words, as a measure of improvement, R Squared says we’re never worse off adding a variable. It can never recommend against adding a variable (until we have k > n, at which point the regression will fail, because X’X cannot be inverted). The Adjusted R Squared is Adjusted R Squared = 1 – (ESS/n-k) / (TSS/n-1). As I have said before, it can be interpreted as subtracting the ratio of two estimates of variance. Like the R Squared, it is 1 if there are no errors.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: But if we add a variable whose t-statistic is less than 1 (in absolute value), then the Adjusted R Squared will decrease. It does balance complexity (more variables in the model) against smaller total squared error. In contrast to every other measure we will see here, we want its maximum rather than its minimum. The AIC The AIC, as Mathematica uses it, appears to be defined as It is more than convenient to use rules at this point, so that I can write symbolic equations involving n, k, and ESS without having Mathematica use the numerical values of them. Let me clear the numerical values… set some rules… then ask for the AIC for the regression (our main one, the Hald data with X1, X2, and X4, which can be found here )… and finally compute it directly using the equation… Additional Selection Criteria...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern