California rain levels. An article published in Geography(July 1980) used multiple regression to predict annual rainfall levels in California. Data on the average annual precipitation (y), altitude 1x12, latitude 1x22, and distance from the Pacific coast 1x32 for 30 meteorological stations scattered throughout California are saved in the CALRAIN file. (Selected observations are listed in the table below.) Consider the first-order model y = b0 + b1 x1 + b2 x2 + b3 x3 + e.

a. Fit the model to the data and give the least squares prediction equation.

b. Is there evidence that the model is useful in predicting annual precipitation y? Test, using a = .05.

c. Find a 95% prediction interval for y for the Giant Forest meteorological station (station 9). Interpret the interval.

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Data for Exercise 12.38 Station 1. Eureka 2. Red Bluff Avg. Annual Precipitation y (inches) 39.57 23.27 3. Thermal 18.20 4. Fort Bragg 37.48 5. Soda Springs 49.26 26. San Diego 9.94 27. Daggett 4.25 28. Death Valley 1.66 29. Crescent City 74.87 30. Colusa 15.95 Altitude (feet) Latitude x2 (degrees) Distance from Coast X3 (miles) 1 97 70 40.8 40.2 33.8 39.4 1 39.3 150 32.7 5 34.1 85 36.5 41.7 194 1 39.2 91