Posted by: tonyteaching | March 27, 2011

Mengukur Pentingnya sebuah Variable dalam Multiple Regression

Yakni dengan melihat selisih nilai R kuadrat pada variable yang diprediksi jika Predictor yang ingin dianalisis TIDAK DIIKUTKAN

Only when it can be assumed that all variables that are correlated with any of the predictor variables and the criterion are included in the analysis can one begin to consider making causal inferences. It is doubtful that this can ever can be assumed validly except in the case of controlled experiments.

One measure of the importance of a variable in prediction is called the “usefulness” of the variable. Usefulness is defined as the drop in the R² that would result if the variable were not included in the regression analysis. For example, consider the problem of predicting college GPA. The multiple R² when College GPA is predicted by High School GPA, SAT, and Letters of recommendation is 0.3997. In a regression analysis conducted predicting College GPA from just High School GPA and SAT, R² = 0.3985. Therefore the usefulness of Letters of Recommendation is only: 0.3997 – 0.3985 = 0.0012.

On the other hand, leaving out SAT and predicting College GPA from High School GPA and Letters of Recommendation yields an R² = 0.3319. Therefore, the usefulness of SAT is 0.3997 – 0.3319 = 0.068.

Selalu diingat bahwa Usefulness sebuah variable lebih tepat mewakili nilai penting variable tersebut dibandingkan Pearson Correlation coeefisient. Karena bisa jadi sebuah Predictor memiliki nilai koefisien Pearson Correlation (misal 0.35), tetapi ketika variable-variable predictor lainnya dimasukkan maka nilai Usefulness nya ternyata 0. Hal ini menunjukkan bahwa memang benar variable predictor tadi berhubungan dengan variable dependent nya tetapi ternyata nilai hubungannya(correlation) tadi bisajadi karena adanya variable perantara lainnya.

It is important to bear in mind that the usefulness of a variable refers specifically to the usefulness of a variable when the other variables are included in the regression equation. For instance, although the Letters of Recommendation add practically nothing to the ability to predict College GPA once High School GPA and SAT are known, they are somewhat predictive of College GPA when taken alone: The Pearson correlation between Letters of Recommendation and College GPA is 0.35.

In sum, the usefulness of a variable refers how much it adds to the predictability of the criterion over and above the other predictor variables in the equation. If two predictor variables are highly correlated, then neither will contribute much to the prediction above and beyond the other.

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