The progress report of a research analyst to the supervisor stated: \"All the es
ID: 3239124 • Letter: T
Question
The progress report of a research analyst to the supervisor stated: "All the estimated regression coefficients in our model with three predictor variables to predict sales arc statistically significant. Our new preliminary model with seven predictor variables, which includes the three variables of our smaller model, is less satisfactory because only two of the seven regression coefficients arc statistically significant. Yet in some initial trials the expanded model is giving more precise sales predictions than the smaller model. The reasons for this anomaly are now being investigated." Comment.Explanation / Answer
Correlation of Regressors: Your regressors may be related to each other, effectively measuring something similar. Say, your model is to explain SALES as a function of INDEPENDENT VARIABLES. Hence, the variables basically "compete" for explaining the SALES, which may, especially in small samples, result in both variables "losing", as none of the effects may be strong enough and sufficiently precisely estimated when controlling for the other to get significant estimates. Essentially, you are asking: what is the positive effect of another INDEPENDENT VARIABLE when holding OTHERS constant, leading to large p-values.
Misspecified models: The underlying theory for t-statistics/p-values requires that you estimate a correctly specified model. Now, if you only regress on one predictor, chances are quite high that that univariate model suffers from omitted variable bias. Hence, all bets are off as to how p-values behave. Basically, you must be careful to trust them when your model is not correct.
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