Do beavers benefit beetles? Researchers laid out 23 circular plots, each 4 meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists believe that the new sprouts from stumps are more tender than other cottonwood growth, so beetles prefer them. If so, more stumps should produce more beetle larvae. Here is computer output for a regression of y = number of beetle larvae on x = number of stumps:

Summary of Fit
RSquare ..................................................... 0.839144
RSquare Adj .............................................. 0.831484
Root Mean Square Error ......................... 6.419386
Mean of Response ................................. 25.086960
Observations (or Sum Wgts) .............................. 23

Parameter Estimates

a. Calculate and interpret the residual for the plot that had 2 stumps and 30 beetle larvae.

b. Interpret the slope.

c. By about how much do the actual number of larvae typically vary from the values predicted by the least-squares regression line with x = number of stumps?

d. What percent of the variability in number of larvae is accounted for by the least-squares regression line with x = number of stumps?

Transcribed Image Text:

Std Error t Ratio Prob>lt| -0.45 Term Estimate Intercept Number of stumps -1.286104 2.853182 0.6568 11.893733 1.136343 10.47 <.0001*