Sunday, December 18th, 2016

A **proper linear model** is one in which the weights given to the predictor variables are chosen in such a way as to optimize the relationship between the prediction and the criterion. The most commong example is simple **regression** analysis in where the predictor variables are weighted in such a way as to maximize the correlation between the subsequent weighted composite and the actual criterion.

An **improper linear model** is one in which the weights are chosen by some nonoptimal method. They may be chosen to be **equal** or they may be chosen on the basis of the **intuition** of the person making the prediction.

The logic of multiple **regression** is unassailable: it finds the optimal formula for putting together a weighted combination of the predictors. However, the complex statistical algorithm adds little or no value. One can do just as well by selecting a set of scores that have some **validity** for predicting the outcome and adjusting the values to make them comparable (by using standards or ranks). A formula that combines these predictors with equal weights is likely to be just **as accurate** in predicting new cases as the multiple-regression formula that was optimal in the original sample. Even more, formulas that assign equal weights to all the predictors are **often superior**, because they are not affected by accidents of sampling.

For example, marital stability is weel predicted by a formula:

Marital Stability = Frequency of Lovemaking – Frequency of Quarrels.

You don’t want your result to be a negative number.

Hundreds of studies have proven that **Proper** Linear Models (regressions, etc.) are better at predicting dependent variables from independent variables than intuitively predicting the dependent variable. But even **Improper** Linear Models (experts define variables as positive or negative and then a simple linear function is built without being regressed) beat experts studying the independent variables and forecasting the outcome (heuristics).

**Summing-up**: an algorithm that is constructed on the back of an evelope is often good enought to compete with an optimally weighted formula, and certainly good enough to outdo expert judgment.

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