The effects of grazing animals on grasslands have been the focus of numerous investigations by ecologists. One such study, reported in “The Ecology of Plants, Large Mammalian Herbivores, and Drought in Yellowstone National Park” (Ecology [1992]: 2043– 2058), proposed using the simple linear regression model to relate y = green biomass concentration (g/cm3) to x 5 elapsed time since snowmelt (days).
a. The estimated regression equation was given as y^ 5 106.3 2 .640x. What is the estimate of average change in biomass concentration associated with a 1-day increase in elapsed time?
b. What value of biomass concentration would you predict when elapsed time is 40 days?
c. The sample size was n = 58, and the reported value of the coefficient of determination was .470. Does this suggest that there is a useful linear relationship between the two variables? Carry out an appropriate test.