Question

Econometric

Explain why it is dangerous to judge the quality of a regression model by maximizing R^2?

You are encouraged to use a hypothetical example in answering this question. (Your answer should be more than 2 sentences long).

*short answer

*hypothetical example

Answer 1

R² tells us about the "GOODNESS OF FIT" of a model. In other words it tells us what percentage variation of independent variable is explained by percentage variation in dependent variable/variables.

In general it is observed that increasing of dependent variable results in increasing of R². While variation of dependent variable is explained by independent variables, not all independent variables may be having a statistically significant impact on the dependent variable. So, individual significance of the independent variables must also be checked by performing t test for each regressors.

So, R² maximization is dangerous to judge quality of a regression model.

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HYPOTHETICAL EXAMPLE

Let us say that we are regressing GDP on consumption i.e.

Y = B1 + B2(C) + U_i

Hypothetical data:

Y	C
420	250
348	123
311	144
432	68
491	103
225	225
148	50
378	186
446	175
156	25
308	144
486	238
254	230
469	224
467	250
436	111
289	80
444	358
350	154
148	100
276	163
366	211
198	171
198	166
295	127
252	183
197	168
342	260
164	88
399	167

As we see Consumption is significant at 5% CI and R square is 0.188.

Now we add another variable, leisure hours i.e. total hours a person sleeps in a day.

Y = B1 + B2(C) + B3(S) + U_i

There is supposed to be no statistically significant relation between leisure hours and GDP.

Hypothetical Data:

Y	C	S
420	250	9
348	123	14
311	144	11
432	68	11
491	103	8
225	225	14
148	50	10
378	186	10
446	175	14
156	25	13
308	144	11
486	238	9
254	230	9
469	224	13
467	250	11
436	111	13
289	80	10
444	358	11
350	154	10
148	100	8
276	163	12
366	211	11
198	171	9
198	166	13
295	127	10
252	183	9
197	168	8
342	260	7
164	88	13
399	167	7

Although R square is higher (0.19>0.188) , S is not statistically significant as P value of test > 0.05.

This proves that Maximizing R square is not a good option to judge quality of model.