Question

Stress can affect the physiology and behavior of animals, just as it can with humans (as many of us know all too well). The accompanying data on \(x=\) plasma cortisol concentration (in milligrams of cortisol per milliliter of plasma) and \(y=\) oxygen consumption rate (in milligrams per kilogram per hour) for juvenile steelhead after three 2-min disturbances were read from a graph in the paper \({ }^{\text {"Metabolic Cost of Acute Physical Stress in Juvenile Steel- }}\) head" (Transactions of the American Fisheries Society [1987]: \(257-263\) ). The paper also included data for unstressed fish. \(\begin{array}{lllllllllll}x & 25 & 36 & 48 & 59 & 62 & 72 & 80 & 100 & 100 & 137\end{array}\) \(\begin{array}{lllllllllll}y & 155 & 184 & 180 & 220 & 280 & 163 & 230 & 222 & 241 & 350\end{array}\) a. Is the value of \(y\) determined solely by the value of \(x\) ? Explain your reasoning. b. Construct a scatterplot of the data. c. Does an increase in plasma cortisol concentration appear to be accompanied by a change in oxygen consumption rate? Comment.

Short answer

The value of \(y\) cannot solely be determined by \(x\), as there can be other variables affecting \(y\). To visualize the relationship, a scatter plot can be drawn with the given values of \(x\), and \(y\). By observing this scatterplot, we can note a trend that might suggest an increase in plasma cortisol concentration results in a change in oxygen consumption rate, but it cannot be definitively confirmed without additional statistical analysis.

Step-by-step solution

Determining the relationship between x and y

For a given set of data points, \(y\) isn't determined solely by the value of \(x\). There might be other factors or variables that could influence the value of \(y\). The relationships between variables are multi-faceted and include factors not accounted for in the provided data.

Constructing a scatter plot

Using a graphical plotting tool, plot the data points individually on a 2D grid using the cortisol concentration as x-coordinate and the oxygen consumption rate as y-coordinate. Each pair of (x,y) defines a point in the 2D grid.

Evaluating correlation

By observing the scatter plot, try to understand the relationship between the cortisol concentration and the oxygen consumption rate. If the points appear to rise from left to right, there might be a positive correlation. If the points fall from left to right, it might suggest a negative correlation. If the points do not follow any clear directional trend, it might signify the absence of a correlation. However, a more detailed statistical analysis would be needed for a definitive answer.