Show that the estimated coefficient for log(ppgdp) is the same as the estimated slope in the added-variable plot for log(ppgdp) after pctUrban. This correctly suggests that all the estimates in a multiple linear regression model are adjusted for all the other regressors in the mean function.
Show that the residuals in the added-variable plot are identical to the residuals from the mean function with both predictors.
Show that the t-test for the coefficient for log(ppgdp) is not quite the same from the added-variable plot and from the regression with both regressors, and explain why they are slightly different.
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