Data on the average annual precipitation (y), altitude (x), latitude (x), and distance from the coast (x3) for a particular state were collected fo meteorological stations. The observations are listed in the table below. Consider the first-order model y = Po + BX + Bx + 3x3 + E. Complet parts a through c. Station 2 3 4 y (in) 40.12 23.45 18.65 38.40 49.64 x (ft) 45 340 4155 71 6757 x () 44.6 40.3 34.0 39.2 39.4 a. Fit the model to the data and give the least squares prediction equation. y = -113.692 + (005) x + (3.560 ) x + (-080) x3 (Round to three decimal places as needed.) A. Ho: B B B3 = 0 H B B B3 #0 B. Ho: B B C. Ho: B B D. Ho: B-B X3 (mi) 2 98 72 2 151 B30, H: At least one B #0, i = 1, 2, 3 B3 =0, H: Exactly one , #0, i=1, 2, 3 B3=0, H: All B 0,i= 1, 2, 3 The test statistic is F = 11.49. (Round to two decimal places as needed.) Station 67890 10 b. Is there evidence that the first-order model is useful for predicting annual precipitation y? Test using a = 0.05. Determine the null and alternative hypotheses. Choose the correct answer below. y (in) 20.44 17.82 13.99 41.28 14.75 The p-value is .007 (Round to three decimal places as needed.) Is there evidence that the first-order model is useful for predicting annual precipitation y? Yes, because the p-value is less than a = 0.05. c. Predict, with 95% confidence, the average annual precipitation for station 2. CD (Round to two decimal places as needed.) x (ft) 54 22 95 6369 73 x () 37.6 38.5 37.5 36.7 36.9 Full data s X3 (n 4 79 29 14 12