The differenced data increases the standard errors on all coefficient estimates, as well as the overall RMSE. This may be the price of correcting a spurious regression. The sign and the size of the coefficient estimate for the undifferenced predictor, AGE, shows little change. Even after differencing, CPF has pronounced significance among the predictors. Accepting the revised model depends on practical considerations like explanatory simplicity and forecast performance, evaluated in the example Time Series Regression VII: Forecasting.