13.7 Using the 50 observations on two variables Y and X shown in the diagram, an investigator runs the following five regressions (standard errors in parentheses; estimation method as indicated;

all variables as logarithms in the logarithmic regressions):

Discuss each of the five regressions, stating, with reasons, which is your preferred specification.

1 2 3 4 5 linear logarithmic OLS AR(1) OLS AR(1) OLS X 0.178 0.223 2.468 2.471 1.280 (0.008) (0.027) (0.029) (0.033) (0.800) Y(-1) 0.092 (0.145) X(-1) 0.966 (0.865) 0.87 0.08 (0.06) (0.14) constant -24.4 -39.7 -11.3 -11.4 -10.3 (2.9) (12.1) (0.2) (0.2) (1.7) R 0.903 0.970 0.993 0.993 0.993 RSS 6286 1932 1.084 1.070 1.020 d 0.35 3.03 1.82 2.04 2.08