The article “The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops (Agric. Meteor. 1974:

375–382) reports the following data on yield (y), mean temperature over the period between date of coming into hops and date of picking (x1), and mean percentage of sunshine during the same period (x2) for the Fuggle variety of hop:

x1 16.7 17.4 18.4 16.8 18.9 17.1 x2 30 42 47 47 43 41 y 210 110 103 103 91 76 x1 17.3 18.2 21.3 21.2 20.7 18.5 x2 48 44 43 50 56 60 y 73 70 68 53 45 31 Here is partial Minitab output from fitting the first-order model used in the article:

Predictor Coef Stdev t-ratio P Constant 415.11 82.52 5.03 0.000 Temp 6.593 4.859 1.36 0.208 Sunshine 4.504 1.071 4.20 0.002 s  24.45 R-sq  76.8% R-sq(adj)  71.6%

a. What is , and what is the corresponding residual?

b. Test versus Ha: either b1 or at level .05.

H0: b1 5 b2 5 0 b2 2 0 mˆ

Y#18.9,43 Y 5 b0 1 b1x 1 1 b2x 2 1 P R SSE 5 203.82 2 5 .456 time 5 75 concentration 5 8 x temperature 5 100 1 5 c5 x 9 5 0 mˆ

Y R b SSE 5 23.379 2 5 .938 ˆ

9 5 22.325, bˆ b 8 5 23.750, ˆ b 7 5 2.975, ˆ b 6 5 24.208, ˆ

5 5 1.867, bˆ b 4 5 22.208, ˆ b 3 5 3.4375, ˆ b 2 5 1.2750, ˆ

1 5 2.8125, b

ˆ x 0 5 21.967, 9 5 x 2x 3 x 3, x 4 5 x 1 2

, x 5 5 x 2 2

, x 6 5 x 3 2

, x 7 5 x 1x 2, x 8 5 x 1x 3 x 1, x 2 k 5 9 , the three values of each variable were coded as 1, 0, and 1, respectively, giving the accompanying data (the valu

c. The estimated standard deviation of when and is 8.20. Use this to obtain a 95% CI for .

d. Use the information in part

(c) to obtain a 95% PI for yield in a future experiment when x1 = 18.9 and .

e. Minitab reported that a 95% PI for yield when and is (35.94, 151.63). What is a 90% PI in this situation?

f. Given that x2 is in the model, would you retain x1?
g. When the model is fit, the resulting value of R2 is .721. Verify that the F statistic for testing versus the alternative hypothesis satisfies , where t is the value of the t statistic from part (f).