Life is a linear regression model

 

Let us take a linear regression model

Y = β₀ + β₁x₁ + β₂x₂ + _ _ _ _ _ _ β_nx_n + u

Where y is the response variable, β (s) are the parameters and x (s) are the input variables.

Now imagine the ingredients of success in any endeavor, work or life in general.

Success = intercept + (factor1)*(amount of work put in) + (facor2) *(relevant experience) + (factor3)*(status/rapport/goodwill) + unobservables

The amazing thing this equation enables us to do is to look at the effects of only one of the factors in terms of its effects, keeping all the other factors and their effects constant.  This enables to look at all the factors which constitute success in an objective way, enabling us to get rid of our biases.

Suppose you are to write an examination in half an hour. This is a very nervous time for us students, and as we know, most of our superstitions and false beliefs creep up in the weakest of our times. You are in your final moments, walking towards the examination hall, and suddenly you realize that you did not bring your identification card with you. Now that you start weighing up the two options you have, running back to your room to get your ID, which will be safer but will make you lose out on time and a lot of energy, versus the riskier option, relying on the leniency of the invigilator or pleading for some consideration. For good or bad, you decide to take the first option and get the ID to the exam. With a drop of sweat on your face you start answering the first question and damn, you could not even move beyond the first step. You are absolutely stuck and decide to move on to question two.

It is a common human tendency to be in a low morale now, and eventually end up ruining all of the answers. Fallacy of composition, that as you were having a bad ‘luck’ till now, this is your bad day, and putting more effort to the rest of the paper is just not worth it, is sure to show up at least once, even in the minds of the most rational thinkers.

But now you remember the regressed equation of what you want to achieve. That your marks depend on so many factors, while each of them are independent. If you can remind yourself that over the time, the unobservables are to have a zero effect, and its ups and downs are to cancel down, in place of falling for the ‘luck’ trap. If you can, with a calm mind, put up an unbiased analysis of the circumstances, you would realize that your chances have not dwindled; if fact the power of your hard work and the practice you went through still remain the same. And as you increase the trials/data points, they will in fact make you reach your desired position. But only if you let them.

Drawing in parallels to the assumptions of the Classical linear regression model, which defines necessary conditions under which a model can be expected to give correct results http://en.wikibooks.org/wiki/Econometric_Theory/Assumptions_of_Classical_Linear_Regression_Model
It can be seen that many of these conditions can be used to explain about the character of the inputs variables of success:
(Note: It must be kept in mind that these are only on an analogy basis, to make us realize the less graspable concepts of the very varied and emotional experiences of life through something you could be using in your everyday life and is not very tough to comprehend. As this is not a mathematical induction proof, one cannot expect all the features of the two cases to match)

·         Sample variation: the inputs cannot remain just the same for all the observations; if they did, there would be no life. It depends on the variation, sometimes intended and mostly unintended, of our inputs, the effort we put in, to have patterns in life. With similarity all across there would be no pattern, no information.

·         Zero conditional mean:  The unobservables, which may consist of the wealth you inherited, genetic advantages and disadvantages. Environmental variables do not lend a significant effect over the population. Even for the life of a single person, the effect of disturbances, those out of your control would drop to zero over the long term. Some would help you, without any deliberation, while others would retard your progress, again without any mistake from your side.

·         Autocorrelation: If the unobervables from subsequent obervations are related to each other, that would eventually mean that you are letting your previous failure or success get to your get. Both of them may have positive or a negative effect, depending on your thought pattern. But on the whole it would be a cleaner way to stop previous results get to your head. Each turn is a whole new game, and you must act up to each one of it.