In a study of the ecology of movement of individuals in small streams, researche

Question

In a study of the ecology of movement of individuals in small streams, researchers tracked the movements of larval red salamanders. They defined “net direction” as the differences in the relative frequency of captures moving upstream and the relative frequency of captures moving downstream. Positive numbers indicate a net movement upstream, negative numbers indicate a net direction downstream. A fit of a simple linear regression model of the net direction as a function of centigrade temperature of water in 14 small streams resulted in the following estimated regression equation: NetDir = -0.14 + 0.016 MeanTemp.

a) How would you interpret the value of b = 0.016?

b) Substituting x = 12 degrees Centigrade gives NetDir = 0.052 . Give two different interpretations of this number.

c) Do you think this equation should be used for predicting movement of red salamanders in large streams? Explain your response in a few sentences.

d) The value of r2 is 0.34. How you would interpret this value in the context of this problem?

Explanation / Answer

a. The regression coefficient, b is 0.016, which implies that with increase in MeanTemp by 1 degree Centigrade, the Net direction is 0.14 units downstream.

b. At a mean temperature of 12 degrees of Centigrade, the Net diretion is 0.052 upstream. With increase in temperature, the net direction turns to be upstream.

c. The linear regression eqaution is based on value sobtained from 14 small streams, which might have different frequency of captures and that too with varied sizes. Therefore, the result cannot be generalized in predicting movement of red salamanders in large streams.

d. Around 34% variation in Net direction of captures in small streams is explained by variation in Mean temperature.

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