Scenario Background: An article published in Geography (July 1980) used multiple regression to predict annual rainfall levels in California. Data on the average annual precipitation, altitude, latitude, and distance from the Pacific coast for 30 meteorological stations scattered throughout California were collected and listed below. Station Name Precipitation 1 Altitude Latitude Eureka Distance 39.57 2 47 Red Bluff 10.7 23.27 1 341 3 10.2 Thermal 97 18.2 4 4152 33.8 Fort Bragg 70 37.48 5 74 39.4 Soda Springs 1 49.26 6 675 39.3 San Francisco 50 21.82 7 52 37.8 5 Sacramento 18.07 25 38.5 San Jose 80 14.17 37.4 Giant Forest 28 42.63 5360 10 36.6 Salinas 145 13.85 11 74 36.7 Fresno 12 9.44 12 331 Pt Piedras 36.7 19.33 114 13 57 35.7 Pasa Robles 1 15.67 740 14 35.7 Bakersfield 31 5.1 15 190 35.3 Bishop 76 5.73 16 4108 37.3 Mineral 198 47.82 17 1850 10.4 Santa Barbara 142 17.91 18 121 34.6 Susanville 1 18.2 4152 19 10.3 Tule Lake 198 10.OE 4036 20 41.9 Needles 140 4.63 21 913 Burbank 34.8 192 14.74 599 22 34.2 Los Angeles 47 15.02 23 312 34.1 Long Beach 16 12.30 50 24 33.8 Los Banos 12 8.21 25 126 Blythe 37.5 75 4.05 268 26 33.6 San Diego 155 9.94 27 19 32. Daggett 5 4.25 28 2105 34.1 Death Valley 85 1.69 29 -175 36.2 Crescent City 194 74.87 35 30 41.7 Colusa 5.95 60 39.2 91Summary of Fit RSquara 0601502 RSquBra AdI Foot Mean Square Error 41 09335 Mean of Response 15 77567 Observations [or Sum Witch 30 Analysis of Variance Sum of Mean aanos OF Squares Square F Ratio Model 4317.85 1812 59 Error 3100.625 121 08 Prob s F C. Total 8087.274 Parameter Estimates Estimate Sid Error Ratio Probalt] Intoreact -101 444 20.12440 20.14101 Latitude 1.70407 1.1 Residual by Predicted Plot BD .10 0 in an an an in 60 70 no Precip Predicted Notes: The "largest" residuals are -28. 8604 and 33.19675. Pizza 2 of 41. Set up a boypothesized first order model and define all variables (a's and y's ) in your model. 1. Use the computer output to fit the model described above. 3. State and interpret the value of pie in the context of this problem. 4. State and interpret the value of fo in the context of this problem. 5. Is altitude a statistically useful predictor of annual rainfall levels? Text at the a =_05 significance level