The data file wa_wheat contains wheat yield for several shires in Western Australia from 1950 to 1997.

a. If the variable YIELD is "average wheat yield" in tonnes per hectare what is the interpretation of RYIELD \(=1 /\) YIELD?

b. For Northampton and Mullewa shires, plot RYIELD \(=1 /\) YIELD against YEAR \(=1949+\) TIME. Do you notice any anomalies in the plots? What years are most unusual? Using your favorite search engine discover what conditions may have affected wheat production in these shires during these years.

c. For Northampton and Mullewa shires, estimate the reciprocal model RYIELD \(=\alpha_{1}+\alpha_{2}\) TIME \(+e\). Interpret the estimated coefficient. What does the sign tell us?

d. For the estimations in part (c), test the hypothesis that the coefficient of TIME is greater than or equal to zero against the alternative that it is negative, at the \(5 \%\) level of significance.

e. For each of the estimations in part (c), calculate studentized residuals, and values for the diagnostics LEVERAGE, DFBETAS, and DFFITS. Identify the years in which these are "large" and include your threshold for what is large.

f. Discarding correct data is hardly ever a good idea, and we recommend that you not do it. Later in this book, you will discover other methods for addressing such problems-such as adding additional explanatory variables-but for now experiment. For each shire, identify the most unusual observation. What grounds did you use for choosing?

g. Drop the most unusual observation for each shire and reestimate the model. How much do the results change? How do these changes relate to the diagnostics in part (e)?