The article “A Simulation-Based Evaluation of Three Cropping Systems on Cracking-Clay Soils in a Summer Rainfall Environment” (Agricultural Meteorology, 1976:

211–229) proposes a quadratic model for the relationship between water supply index (x) and farm wheat yield (y).

Representative data and the resulting MINITAB output follow:

x | 1.2 1.3 1.5 1.8 2.1 2.3 2.5 y | 790 950 740 1230 1000 1465 1370 x | 2.9 3.1 3.2 3.3 3.9 4.0 4.3 y | 1420 1625 1600 1720 1500 1550 1560 The regression equation is yield
252 1000 index  135 indexsqd Predictor Coef Stdev t-ratio p Constant 251.6 285.1 0.88 0.396 Index 1000.1 229.5 4.36 0.001 Indexsqd 135.44 41.97 3.23 0.008 s
135.6 R-sq
85.3% R-sq(adj)
82.6%

Analysis of Variance SOURCE DF SS MS F p Regression 2 1170208 585104 31.83 0.000 Error 11 202228 18384 Total 13 1372435

a. Interpret the value of the coefficient of multiple determination.

b. Calculate a 95% CI for the coefficient of the quadratic predictor.