# The authors of the paper Evaluating Existing Movement Hypotheses in Linear Systems Using Larval Stream Salamanders (Canadian

## Question:

The authors of the paper €œEvaluating 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 = mean water temperature (°C) and y = 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.

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 = net directionality and x = 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 €œwhen 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?

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