6. Test whether 1

.

7. Construct and interpret a 95% confidence interval for 2.

8. Is the overall model statistically useful for predicting annual rainfall levels? Test at the = .05 significance level.

9. State and interpret the multiple coefficient of determination, 2.

10. Interpret the residual plot for this model and identify any potential outliers.

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 Altitude | Latitude 1 Distance Eureka 19.5 2 Red Bluff 23.27 341 3 40.2 97 Thermal 18.2 4152 33.8 4 70 Fort Bragg 37.48 74 39.4 Soda Springs 19.26 6752 39.3 6 150 San Francisco 21.82 52 37.8 Sacramento 18.07 25 38.5 80 San Jose 14.17 95 37.4 28 Giant Forest 12.63 5360 10 36.6 145 Salinas 13.8: 74 36.7 12 Fresno 36.7 12 114 Pt Piedras 19.33 57 35.7 13 Pasa Robles 15.67 740 14 35.7 31 Bakersfield 190 35.3 15 76 Bishop 5.73 37.3 16 198 Mineral 47.82 4850 40.4 17 142 Santa Barbara 17.9 121 34.6 Susanville 18.2 4152 40.3 19 198 Tule Lake 10.03 4036 41.9 20 140 Needles 163 913 34.8 21 192 Burbank 14.74 509 34.2 22 47 Los Angeles 15.02 23 312 34.1 16 Long Beach 12.36 50 33.8 24 12 Los Banos 8.22 126 25 37.5 75 Blythe 4.0 168 33.6 26 155 San Diego 9194 19 27 327 5 Daggett 4.25 2105 34.1 85 28 Death Valley 1.69 -175 36.2 29 194 Crescent City 74.87 35 41.7 30 1 Colusa 15.95 39.2 91 Page 1 of 4summary of Fit RSquare 0.601902 RSquare Adj 0.555967 Root Mean Square Error 11.09335 Mean of Response 19.77567 Observations [or Sum Wits) 30 Analysis of Variance Sum of Mean Source DF Squares Square F Ratio Model E 4837.65 1612.55 13.1035 Error 26 3199.625 123.06 Prob > F C. Total 8037.274 4.0001 Parameter Estimates Term Estimate Sed Error t Ratio Probsit| Intercept -103.444 29.32445 -3.53 0.0016 Distance -0.14101 0.036301 -3.88 0.0006 Latitude 3.480 026 0.79807 4.36 0.0002 Altitude 0.004029 0.00122 3.1 0.0028 Residual by Predicted Plot 40 30 20 Precip Residual -20 -30 -10 0 10 20 30 40 50 60 70 80 Precip Predicted Notes: The "largest" residuals are -28. 8604 and 33.19675