This analysis compares the model in the text that has the level of shipments as the response to a model that uses the change in the shipments as the response. (These data are monthly, based on the...

This analysis compares the model in the text that has the level of shipments as the response to a model that uses the change in the shipments as the response. (These data are monthly, based on the seasonally adjusted data from 2002 through 2009.) Modeling changes is often more interesting than modeling levels. After all, we often care more about how the future differs from the present than anything else. This scatterplot and table summarize the fit of a regression of the changes,
 -
, in the shipments on the lag of the shipments.

(a) Why do we have 96 observations for fitting this model, even though we need prior values of the response to find the change and the lagged predictor? Shouldn’t we lose one observation from lagging the variable?

(b) How do the slope and intercept of this equation differ from those for the first-order autoregression of the level of shipments on its lag (shown in Table 3)?

(c) Compare
 from this regression to that of the autoregression for the level of shipments. Explain any differences or similarities.

(d) This model has a small
 with a slope that is not statistically significant. Why is the fit of this model so poor, whereas that of the AR(1) model is so impressive?