91Ó°ÊÓ

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 "Metabolic Cost of Acute Physical Stress in Juvenile Steelhead" (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.

Step by step solution

01

Determine the relationship between x and y

From the given data, it is not clear that the value of y (oxygen consumption rate) is solely determined by the value of x (plasma cortisol concentration). This is because one can have many factors influencing the oxygen consumption rate other than the cortisol concentration, such as body weight, activity level, metabolic rate and so on.

02

Construct a scatterplot of the data

Use a scientific plotting software or tool to create a scatterplot. Each point on the scatterplot represents a single observation from the data set, where the x-coordinate of the point equals the cortisol level (x) and the y-coordinate equals the corresponding oxygen consumption rate (y). The scatterplot will help visualize any possible relationship between x and y.

03

Analyze the scatterplot

Look at the scatterplot, if most of the points are coherently distributed around a line (either increasing or decreasing), then there might be a positive or negative correlation between x and y. If the points are randomly scattered without any apparent trend, it suggests no correlation exists between x and y. Remember that correlation does not imply causality.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Scatterplot

A scatterplot is a graphical representation used to visualize the relationship between two variables. In this exercise, we plot plasma cortisol concentration on the x-axis and oxygen consumption rate on the y-axis. Each data point on the scatterplot represents a pair of the two values.

To create a scatterplot, you can use software such as Microsoft Excel, Google Sheets, or statistical software like R or Python libraries (Matplotlib, Seaborn). Simply input the data, and choose the appropriate chart type.

• Scatterplots can reveal the type of relationship (linear or non-linear) between variables.
• Look at how tightly the data points cluster: a tighter cluster often indicates a stronger relationship.
• They help detect outliers, which are data points that don't follow the expected pattern.

By understanding the scatterplot, you can begin to interpret the data interaction and hypothesize any underlying relationships.

Correlation

Correlation analyzes the relationship strength between two variables. It is often represented by the correlation coefficient, with values ranging from -1 to 1. A positive correlation coefficient indicates that as one variable increases, the other tends to also increase, while a negative coefficient indicates an inverse relationship.

In the context of this exercise:

• Check if plasma cortisol concentration and oxygen consumption rate show any tendency to increase or decrease together.
• If the scatterplot demonstrates a pattern where points follow an upward or downward sloping line, it indicates a potential positive or negative correlation, respectively.

Note that correlation only suggests a possible association between two variables. It does not confirm causality, meaning one factor necessarily causes the other to change.

Data Analysis

Data analysis involves examining, transforming, and arranging data to extract useful information and make conclusions. In this scenario, we aim to understand if there is any pattern between cortisol concentration and oxygen consumption rate.

Here's how to proceed with data analysis in this instance:

• Start by visually inspecting the scatterplot to see any obvious patterns or trends.
• Calculate the correlation coefficient to determine the strength and direction of the relationship between the variables.
• Consider using statistical tests to further analyze data significance and the predictability of changes in one variable based on another.

Ultimately, data analysis helps in determining statistical relationships and predicting outcomes based on observed data.

Cortisol Concentration

Cortisol is often referred to as the "stress hormone," as its levels increase in response to stress. In this exercise, plasma cortisol concentration is examined for its potential impact on the oxygen consumption rate of juvenile steelhead fishes.

Understanding cortisol and its role:

• Cortisol is secreted by the adrenal glands and plays a role in various physiological processes, including metabolism and the immune response.
• Elevated cortisol levels may indicate acute stress, which can affect an organism's metabolism, potentially influencing oxygen consumption.

By studying the relationship between cortisol and oxygen consumption, researchers can gain insights into the physiological impacts of stress on animal behaviour and health, enabling better management or treatment strategies in both animals and humans.