117. The article Determination of Biological Maturity and Effect of Harvesting and Drying Conditions on Milling Quality of Paddy (J. Agric. Engrg. Res., 1975: 353—361) reported the following data on date of harvesting (x, the number of days after owering) and yield of paddy, a grain farmed in India (y, in kg/ha).

x 16 18 20 22 24 26 28 30 y 2508 2518 3304 3423 3057 3190 3500 3883 x 32 34 36 38 40 42 44 46 y 3823 3646 3708 3333 3517 3241 3103 2776

a. Construct a scatter plot of the data. What model is suggested by the plot?

b. Use a statistical software package to t the model suggested in

(a) and test its utility.

c. Use the software package to obtain a prediction interval for yield when the crop is harvested 25 days after owering, and also a con dence interval for expected yield in situations where the crop is harvested 25 days after owering.
How do these two intervals compare to one another?
Is this result consistent with what you learned in simple linear regression? Explain.

d. Use the software package to obtain a PI and CI when x  40. How do these intervals compare to the corresponding intervals obtained in (c)?
Is this result consistent with what you learned in simple linear regression? Explain.

e. Carry out a test of hypotheses to decide whether the quadratic predictor in the model t in (b)
provides useful information about yield (presuming that the linear predictor remains in the model).