It may seem odd, but one of the ways biologists can tell how old a lobster is involves measuring the concentration of a pigment called neurolipofuscin in the eyestalk of a lobster. (We are not making this up!) Biologists wondered if it was sufficient to measure the pigment in just one eye stalk, which would be the case if there is a strong relationship between the concentration in the right and left eyestalks. Suppose pigment concentration (as a percentage of tissue sample) was measured in both eyestalks for 39 lobsters, resulting in the following summary quantities. n= 39Σx= 86.8Σy= 84.1 Σxy= 281.1Σx2= 286.0Σy2= 284.8An alternative formula for computing the correlation coefficient that is based on raw data and is algebraically equivalent to the one given in the text is r = Σxy − (Σx)(Σy)n Σx2 − (Σx)2n Σy2 − (Σy)2n.Use this formula to calculate the value of the correlation coefficient. (Round your answer to three decimal places.) r = Interpret this value. There is no linear relationship between the concentrations of neurolipofuscin in the right and left eyestalks. There is a strong negative linear relationship between the concentrations of neurolipofuscin in the right and left eyestalks. There is a weak negative linear relationship between the concentrations of neurolipofuscin in the right and left eyestalks. There is a weak positive linear relationship between the concentrations of neurolipofuscin in the right and left eyestalks. There is a strong positive linear relationship between the concentrations of neurolipofuscin in the right and left eyestal
It may seem odd, but one of the ways biologists can tell how old a lobster is involves measuring the concentration of a pigment called neurolipofuscin in the eyestalk of a lobster. (We are not making this up!) Biologists wondered if it was sufficient to measure the pigment in just one eye stalk, which would be the case if there is a strong relationship between the concentration in the right and left eyestalks.
Suppose pigment concentration (as a percentage of tissue sample) was measured in both eyestalks for 39 lobsters, resulting in the following summary quantities.
n
=
39
Σx
=
86.8
Σy
=
84.1
Σxy
=
281.1
Σx2
=
286.0
Σy2
=
284.8
An alternative formula for computing the
r =
Σxy −
(Σx)(Σy)
n
Σx2 −
(Σx)2
n
Σy2 −
(Σy)2
n
.
Use this formula to calculate the value of the correlation coefficient. (Round your answer to three decimal places.)
r =
Interpret this value.
There is no linear relationship between the concentrations of neurolipofuscin in the right and left eyestalks.
There is a strong negative linear relationship between the concentrations of neurolipofuscin in the right and left eyestalks.
There is a weak negative linear relationship between the concentrations of neurolipofuscin in the right and left eyestalks.
There is a weak positive linear relationship between the concentrations of neurolipofuscin in the right and left eyestalks.
There is a strong positive linear relationship between the concentrations of neurolipofuscin in the right and left eyestal
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