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 to whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures appear below (from a graph in the paper). The two variables of interest are mean water temperature (° C) and net directionality, which was defined as the difference in the relative frequency of released larvae moving upstream and the relative frequency of released larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value means a higher proportion were moving downstream.
a. If the goal is to learn about how net directionality is related to mean temperature, which of these two variables is the response variable and which is the predictor variable?
b. Construct a scatterplot of the data. How would you describe the relationship between these two variables?
c. Find the equation of the least squares line describing the relationship between y = net directionality and x = mean water temperature.
d. Interpret the slope of the least squares regression line in the context of this study.
e. Does it make sense to interpret the intercept of the least squares regression line? If so, give an interpretation. If not, explain why.
f. What value of net directionality would you predict for a stream that had a mean water temperature of 15° C?
g. 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?