Question

Assume you run a regression on two different models (sets of independent variables). The first model results in an ?2R2 of 0.60 and the second model results in an ?2R2 of 0.64. This would mean that

Select one:

a. The independent variables in the first model are not statistically significant, despite what the t-stats and p-values suggest.

b. The second model has better overall explanatory power, but a better ?2R2 is only gained at the expense of other factors. The first model is better at explaining individual coefficient estimates than the second.

c. The second model has higher overall explanatory power, but whether it is a "better" model than the first model depends on other factors too (expected signs of the coefficients, significant t-stats/p-values, etc.).

d. The second model is unambiguously better; since ?2R2 signifies the explanatory power of the entire model, the second model's other results (expected signs, t-stats/p-values) are not as important. The first model should be seen as inferior.

Answer 1

Assume you run a regression on two different models (sets of independent variables). The first model results in an R² of 0.60 and the second model results in an R² of 0.64. This would mean that

Correct choice:

c) The second model has higher overall explanatory power, but whether it is a "better" model than the first model depends on other factors too (expected signs of the coefficients, significant t-stats/p-values, etc.).

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Explanation:

A higher R² value indicates higher explanatory power, but it doesn't mean that the model is unconditionally better. The other vital components are the coefficients, t-values, p-values, F-value, error terms, and so on.

Without further information on these components, no further statement can be made. Tests of significance are also required to compare the two models. It may also be necessary to drop or add a few variables, to further refine the model. None of the two is "inferior", as model building is a process of trial and error. Each step provides more information.