The paper “Commercially Available Plant Growth Regulators and Promoters Modify Bulk Tissue Abscisic Acid Concentrations in Spring Barley, but not Root Growth and Yield Response to Drought” (Ap plied Biology [2006]: 291–304) describes a study of the drought response of barley. The accompanying data on x days after sowing and y soil moisture deficit (in mm)
was read from a graph that appeared in the paper.
Days After Sowing Soil Moisture Deficit 37 0.00 63 69.36 68 79.15 75 85.11 82 93.19 98 104.26 104 108.94 111 112.34 132 115.74

a. Construct a scatterplot of y soil moisture deficit versus x days after sowing. Does the relationship between these two variables appear to be linear or nonlinear?

b. Fit a least-squares line to the given data and construct a residual plot. Does the residual plot support your conclusion in Part (a)? Explain.

c. Consider transforming the data by leaving y un-
changed and using either xr 5 !x or xs 5 1 x .
Which of these transformations would you recommend? Justify your choice using appropriate graphical displays.

d. Using the transformation you recommend in Part (c), find the equation of the least-squares line that describes the relationship between y and the transformed x. y^ 5 166.490 2 6109.4791 1

x2

e. What would you predict for soil moisture deficit 50 days after sowing? For 100 days after sowing?

f. Explain why it would not be reasonable to predict soil moisture deficit 200 days after sowing.