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(c) What value of net directionality would you predict for a stream that had mean water temperature of 9°C? (Round your answer to five decimal places.) 0.58915 X

(c) What value of net directionality would you predict for a stream that had mean water temperature of 9°C? (Round your answer to five decimal places.) 0.58915 X

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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The authors of the paper "Evaluating Existing Movement Hypotheses in Linear Systems Using Larval Stream Salamanders"+ 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. Mean Temperature (x) Net Directionality (y) 6.17 -0.08 8.06 0.25 8.62 -0.14 10.56 0.00 12.45 0.08 11.99 0.03 12.50 -0.07 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
Transcribed Image Text:The authors of the paper "Evaluating Existing Movement Hypotheses in Linear Systems Using Larval Stream Salamanders"+ 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. Mean Temperature (x) Net Directionality (y) 6.17 -0.08 8.06 0.25 8.62 -0.14 10.56 0.00 12.45 0.08 11.99 0.03 12.50 -0.07 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
(c) What value of net directionality would you predict for a stream that had mean water temperature of 9°C? (Round your answer to five decimal places.) 0.58915 X (d) The authors state that "when temperatures were warmer, more larvae were captured moving upstream, but when
Transcribed Image Text:(c) What value of net directionality would you predict for a stream that had mean water temperature of 9°C? (Round your answer to five decimal places.) 0.58915 X (d) The authors state that "when temperatures were warmer, more larvae were captured moving upstream, but when
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