Heteroskedasticity

HETEROSKEDASTICITY:

Is your JOY heteroskedastic? or homoskedastic?

*The homoskedasticity assumption states that “the variance of the unobservable error, u, conditional on the explanatory variables, is constant.”

Var (u | x1 , … , xk) = σ2

In the equation

wage = β0 + β1 educ + β2 exper + β3 tenure + u ,

homoskedasticity requires that the variance of the unobserved error u does not depend on the levels of education, experience, or tenure.

Homoskedasticity fails whenever the variance of the unobservables changes across different segments of the population, where the segments are determined by the different values of the explanatory variables.

For example, in a savings equation, heteroskedasticity is present if the variance of the unobserved factors affecting savings is not constant, e.g., increases with income.

Is your JOY heteroskedastic? or homoskedastic?

Joy equation

In the JOY equation above, our Model predicts that your level of Cheerfulness is a function of: wealth (the amount of money you have in your pocket), grace (which presumably is a function of how much you pray and your closeness to Jesus Christ and His mercy towards you), ambience (a.k.a. the environment or your surroundings), and struggle (the amount of fight [lucha], interior and exterior, you put in.  [What do you think are the magnitude and direction (+ or ) of β1, β2, β3, and β4?]

The error term, u, is supposed to capture all the other factors that explain ‘Joy’ that we may have failed to account for in our Model.  We can never really tell what we may have missed out on, unless we go on a Sherlock Holmes trek toward capturing what those true factors are in the population….

Let’s just hypothesize, for now, that one such factor is “doing an insanity-causing PhD [coursework or DISSERTATION]”.  Let’s set aside for the moment what the beta-coefficient of such a variable would be (although I surmise it’s a resounding NEGATIVE…).  Heteroskedasticity would be present if the variance in such an unobserved factor were to be non-constant, that is, it does not remain the same, i.e., σ2.

In layman’s terms: the “insanity-causing PhD” makes my life go haywire, and my relationship with it goes on a rollercoaster ride! 😦  ¿Entiendes? So, I therefore conclude … that my JOY is … heteroskedastic!!! Boo-hoo! T.T

Cosa facciamo? ¿Qué hacer? Hmm, I know! I’ve found another ‘hidden explanatory factor’ for our ‘Joy equation’ above: MUSIC!!! Let’s sing! ¡Vamos a cantar! Do you know the song “I Will Sing Forever”?  Here goes:

http://www.storage.to/get/2iC5q37Q/I_Will_Sing_Forever___Full.MID

(If you have Finale Notepad, & you can’t find the score on the Internet, I can send you the Music Sheet (.mus file). Drop me an email…)

I WILL SING FOREVER OF YOUR LOVE, O LORD:

I will sing forever of Your love, O Lord;

I will celebrate the wonder of Your name;

For the word that You speak

is a song of forgiveness

and a song of gentle mercy and of peace.

Let us wake at the morning and be filled with Your love

and sing songs of praise all our days,

For Your love is as high as the heavens above us

and Your faithfulness as certain as the dawn.

I will sing forever of Your love, O Lord;

for You are my refuge and my strength

You fill the world with Your life-giving Spirit

that speaks Your word,

Your word of mercy and of peace.

And I will sing forever of Your love, O Lord

Yes, I will sing forever of Your love, O Lord!

🙂  🙂  🙂

I saw this just now, on “PhD Comics” group in FB,

in answer to the Forum question “You know you’re a PhD student when…”

“…you realize that you must use non-parametric test because the Ph.D life is not normally distributed”.  Hahaha!

PhD-comic-4

http://www.phdcomics.com/

PhD-comic-3

🙂  🙂  🙂