12.69 Nematodes Some varieties of nematodes, roundworms that live in the soil and frequently are so small as to be invisible to the naked eye, feed on the roots of lawn grasses and other plants. This pest, which is particularly troublesome in warm climates, can be treated by the application of nematicides. Data collected on the percent kill of nematodes for various rates of application (dosages given in kg per hectare of active ingredient) are as follows:

Use an appropriate computer printout to answer these questions:

a. Calculate the coefficient of correlation between rates of application.x and percent kill y.

b. Calculate the coefficient of determination, and interpret.

c. Fit a least-squares line to the data.

d. Suppose you wish to estimate the mean percent kill for an application of 1.82 kg of the nematicide per hectare. What do the diagnostic plots generated by MINITAB tell you about the validity of the regression assumptions? Which assumptions may have been violated? Can you explain why?

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Residual Rate of application, x 2 Percent kill, y 3 4 5 50, 56, 48 63, 69, 71 86, 82, 76 94, 99, 97 MINITAB diagnostic plots for Exercise 12.69 Normal Probability Plot of the Residuals (response is y) Percent 99- 95- 90- 80- 70+ 60- 50 40-i 30- 20- 10- 5 -10 50- 2.5- 0.0- -2.5- -5.0- -8 50 Residual Residuals versus the Fitted Values (response is y) 60 70 Fitted Value 80 -8 8- 100