The article “The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops (Agricultural Meteorology, 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 Y
0 1x1 2x2 ! 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 ˆ Y18.9,43, and what is the corresponding residual?

b. Test H0: 1
2
0 versus Ha: either 1 or 2 0 at level .05.

c. The estimated standard deviation of ˆ

0 ˆ

1x1 ˆ

2x2 when x1
18.9 and x2
43 is 8.20. Use this to obtain a 95% CI for Y18.9,43.

d. Use the information in part

(c) to obtain a 95% PI for yield in a future experiment when x1
18.9 and x2
43.

e. MINITAB reported that a 95% PI for yield when x1
18 and x2
45 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 Y
0 2x2 ! is fit, the resulting value of R2 is .721. Verify that the F statistic for testing H0: Y
0 2 x2 ! versus Ha: Y
0 1x1

2 x2 ! satisfies t 2

f, where t is the value of the t statistic from part (f).