Weed Competition Problem: In the report Applications of Mathematics: A Nationwide

Chapter 8, Problem 4

(choose chapter or problem)

Weed Competition Problem: In the report Applications of Mathematics: A Nationwide Survey, submitted to the Ministry of Education, Ontario (1976), A. C. Madgett reports on competition of wild oats (a weed) with various crops. The more wild oats that are growing with a crop, the greater the loss in yield of that crop. Figure 8-4i and the table show information gleaned from pages II-8 to II-10 of that report. 1 3 5 8 10 10 20 17 50 25 100 34 150 40 200 48 Figure 8-4i a. From the scatter plot, tell what kind of function is most likely to fit the data. By regression, find the particular equation of this kind of function. Plot it and the scatter plot on the same screen. Sketch the result. b. Make a residual plot. Sketch the result. What information do you get about the way your selected function fits the data from the residual plot? From the correlation coefficient? c. Based on your mathematical model, what percent of crop loss would be expected for 500 wild oat plants per square meter? Do you find this number by extrapolation or by interpolation? d. How many wild oat plants per square meter do you predict it would take to choke out the wheat crop completely? Do you find this number by extrapolation or by interpolation?