36 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 (x1), latitude (x2), and distance from the Pacific coast (x3) for 30 meteorological stations scattered throughout California are saved in the CALIRAIN file. (Selected observations are listed in the table above.) 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 36 Station Avg. Annual Precipitation y (inches) Altitude X1 (feet) 1. Eureka 39.57 43 40.8 Latitude X2 (degrees) Distance from Coast X3 (miles) 1 2. Red Bluff 23.27 341 40.2 97 3. Thermal 18.20 4152 33.8 70 4. Fort Bragg 37.48 74 39.4 1 5. Soda Springs 49.26 6752 39.3 150 26. San Diego 9.94 19 32.7 5 27. Daggett 4.25 2105 34.1 85 28. Death Valley 1.66 -178 36.5 194 29. Crescent City 74.87 35 41.7 1 30. Colusa 15.95 60 39.2 91 Source: Taylor, P. I. "A pedagogic application of multiple regression analysis." Geography, July 1980, Vol. 65, pp. 203-212. Reprinted with permission from the author.