Round to three decimal places if it is necessary. 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 1 Name Eureka Precipitation Altitude Latitude Distance 39.57 42 40.7 1 2 Red Bluff 23.27 341 40.2 97 3 Thermal 18.2 4152 33.8 70 4 Fort Bragg 37.48 74 39.4 1 5 Soda Springs 49.26 6752 39.3 150 6 San Francisco 21.82 52 37.8 5 7 Sacramento 18.07 25 38.5 80 8 San Jose 14.17 95 37.4 28 9 Giant Forest 42.63 6360 36.6 145 10 Salinas 13.85 74 36.7 12 11 Fresno 9.44 331 36.7 114 12 Pt Piedras 19.33 57 35.7 1 13 Pasa Robles 15.67 740 35.7 31 14 Bakersfield 5.1 490 35.3 76 15 Bishop 5.73 4108 37.3 198 16 Mineral 47.82 4850 40.41 142 17 Santa Barbara 17.91 121 34.6 1 18 Susanville 18.2 4152 40.3 198 19 Tule Lake 10.03 4036 41.9 140 20 Needles 4.63 913 34.8 192 21 Burbank 14.74 699 34.2 47 22 Los Angeles 15.02 312 34.1 16 23 Long Beach 12.36 50 33.8 12 24 Los Banos 8.22 126 37.5 75 25 Blythe 4.05 268 33.6 155 26 San Diego 9.94 19 32.7 5 27 Daggett 4.25 2105 34.1 85 28 Death Valley 1.69 -175 36.2 194 29 Crescent City 74.87 35 41.7 1 30 Colusa 15.95 60 39.2 91 Summary of Fit RSquare 0.601902 RSquare Adj 0.555967 Root Mean Square Error 11.09335 Mean of Response 19.77567 Observations (or Sum Wgts) 30 Analysis of Variance Source Model Error C. Total Parameter Estimates Term Intercept Distance Latitude Altitude Residual by Predicted Plot Precip Residual 40- 30- 20- 10- 0 -10- Sum of Mean DF Squares Square F Ratio 3 4837.65 1612.55 13.1035 26 3199.625 123.06 29 8037.274 Prob > F |t| -3.53 0.0016 -3.88 0.0006 4.36 0.0002 3.3 0.0028 -20- -30- -10 10 20 30 40 50 60 70 80 Precip Predicted Notes: The "largest" residuals are -28. 8604 and 33.19675. Station Name Lower 95% Mean Precip Upper 95% Mean Precip Lower 95% Indiv Precip Upper 95% Indiv Precip Eureka 28.93574 47.50713 13.60055 62.84232 Red Bluff 16.27748 32.02089 0.026014 48.27236 Thermal 10.44318 31.63743 -4.10453 46.18514 Fort Bragg 25.97636 41.67632 9.710248 57.94243 Soda Springs 27.466 51.28601 13.6503 65.10171 San Francisco 21.13974 34.07148 3.903896 51.30732 Sacramento 13.1768 25.53728 -4.26835 42.98243 San Jose 17.69665 28.59059 -0.30064 46.58788 Giant Forest 17.59199 40.61895 3.560919 54.65002 Salinas 17.03587 28.72244 -0.66034 46.41865 Fresno 3.315116 15.74813 -14.1033 33.16653 Pt Piedras 14.40953 27.35397 -2.8217 44.58519 Pasa Robles 13.99887 24.80813 -4.03096 42.83796 Bakersfield 5.43124 15.88609 -12.7356 34.05289 Bishop 6.388762 23.59873 -9.37857 39.36605 Mineral 27.63959 45.69685 12.14314 61.19331 Santa Barbara 10.20865 24.41455 -6.57178 41.19498 Susanville 16.18607 35.03616 0.937336 50.28489 Tule Lake 29.31286 48.46786 14.15795 63.62278 Needles -16.4115 4.943199 -30.9129 19.4446 Burbank 5.504134 18.02004 -11.8838 35.40793 Los Angeles 7.194043 21.25804 -9.63633 38.08841 Long Beach 5.292725 20.08802 -11.2823 36.66305 Los Banos 11.71253 22.26554 -6.41621 40.39427 Blythe -17.3956 2.812139 -32.2327 17.64923 San Diego 0.917639 18.53138 -14.7198 34.16883 Daggett 4.940058 18.50194 -12.0686 35.5106 Death Valley -17.5363 6.48012 -31.2994 20.24322 Crescent City 31.12358 52.22293 16.54837 66.79813 Colusa 13.34241 27.42353 -3.48193 44.24786 You are going to fit a multiple regression model which includes Distance, Latitude, and Altitude as the independent variables and Precipitation as the dependent variable. 1. Set up a hypothesized first order model and define all variables (x's and y's) in your model.(10 points) 2. State and interpret the value of 3 in the context of this problem.(10 points) 3. Is altitude a statistically useful predictor of annual rainfall levels? Test at the a= .05 significance level. (10 points) 4. Test whether B <0 at the a=.05 significance level.(15 points) 5. Construct and interpret a 95% confidence interval for B-(10 points) 6. Is the overall model statistically useful for predicting annual rainfall levels? Test at the a=.05 significance level.(15 points) 7. State and interpret the multiple coefficient of determination, R. (10 points) 8. Interpret the residual plot for this model and identify any potential outliers. (10 points) 9. State and interpret the 95% confidence interval for E(y) in the context of the problem when a station's distance is 1, latitude is 34.6, and altitude is 121.(10 points) Bonus Is there a linear correlation between distance and altitude? Test at a = .05.(5 points)