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.

Station Avg. Annual Precipitation y (inches)
Altitude x1 (feet)
Latitude x2 (degrees)
Distance from Coast x3 (miles)
1. Eureka 39.57 43 40.8 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 f f f f f 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