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 (°C) 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 0.08 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 °C?

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?

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