5.16 ● The authors of the paper “Evaluating Existing Movement Hypotheses in Linear Systems Using Larval Stream Salamanders” (Canadian Journal of Zoology [2009]:

292–298) investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream.

Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper).

The two variables of interest are x 5 mean water temperature (8C) and y 5 net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream.
Mean Temperature (x) Net Directionality (y)
6.17 20.08 8.06 0.25 8.62 20.14 10.56 0.00 12.45 0.08 11.99 0.03 12.50 20.07 17.98 0.29 18.29 0.23 19.89 0.24 20.25 0.19 19.07 0.14 17.73 0.05 19.62 0.07

a. Construct a scatterplot of the data. How would you describe the relationship between x and y?

b. Find the equation of the least-squares line describing the relationship between y 5 net directionality and x 5 mean water temperature.

c. What value of net directionality would you predict for a stream that had mean water temperature of 15 8C?

d. The authors state that “when temperatures were warmer, more larvae were captured moving upstream, but when temperatures were cooler, more larvae were captured moving downstream.”
Do the scatterplot and least-squares line support this statement? Explain.

e. Approximately what mean temperature would result in a prediction of the same number of salamander larvae moving upstream and downstream?