McCullom’s International Grains is constantly searching out areas in which to expand its market. Such markets present different challenges since tastes in the international market are often different from domestic tastes. India is one country on which McCullom’s has recently focused. Paddy is a grain used widely in India, but its characteristics are unknown to McCullom’s. Charles Walters has been assigned to take charge of the handling of this grain. He has researched its various characteristics. During his research he came across an article, “Determination of Biological Maturity and Effect of Harvesting and Drying Conditions on Milling Quality of Paddy” [Journal of Agricultural Engineering Research (1975), pp. 353–361], which examines the relationship between y, the yield (kg/ha) of paddy, as a function of x, and the number of days after flowering at which harvesting took place. The accompanying data appeared in the article and are in a file called Paddy.
y x
2,508…………….16
2,518…………….18
3,304…………….20
3,423…………….22
3,057…………….24
3,190…………….26
3,500…………….28
3,883…………….30
3,823…………….32
3,646…………….34
3,708…………….36
3,333…………….38
3,517…………….40
3,241…………….42
3,103…………….44
2,776…………….46
a. Construct a scatter plot of the yield (kg/ha) of paddy as a function of the number of days after flowering at which harvesting took place. Display at least two models that would explain the relationship you see in the scatter plot.
b. Conduct tests of hypotheses to determine if the models you selected are useful in predicting the yield of paddy.
c. Consider the model that includes the second-order term x2. Would a simple linear regression model be preferable to the model containing the second-order term? Conduct a hypothesis test using the p-value approach to arrive at your answer.
d. Which model should Charles use to predict the yield of paddy? Explain your answer.