[DATA] Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground cricket.
a. What is the most likely explanatory variable in these data? Explain your reasoning.

Verified step by step guidance

1. Step 1: Understand the variables given in the data. We have two variables: Temperature (in degrees Fahrenheit) and Chirps per Second (number of chirps the cricket makes per second).
2. Step 2: Identify the explanatory variable. The explanatory variable is the one that is presumed to cause or explain changes in another variable. In this context, temperature is likely the explanatory variable because it is reasonable to think that changes in temperature affect the cricket's chirping rate.
3. Step 3: Identify the response variable. The response variable is the outcome or the variable that is affected by the explanatory variable. Here, the number of chirps per second is the response variable because it changes in response to temperature.
4. Step 4: Justify the choice of explanatory variable. Since temperature is an environmental condition that can influence the cricket's behavior, it makes sense to consider temperature as the explanatory variable and chirps per second as the response variable.
5. Step 5: Summarize the reasoning. Therefore, the most likely explanatory variable in these data is temperature because it is the factor that potentially influences the number of chirps per second made by the cricket.

Key Concepts

Explanatory and Response Variables

In a study, the explanatory variable is the one that is presumed to influence or predict changes in another variable, called the response variable. Here, temperature is likely the explanatory variable because it is thought to affect the number of cricket chirps, which is the response variable.

Paired Data and Relationship Analysis

Paired data consist of two related measurements for each subject or unit, such as temperature and chirps per second for crickets. Analyzing paired data helps identify patterns or relationships, such as whether chirp rate increases as temperature rises.

Correlation and Causation

Correlation measures the strength and direction of a linear relationship between two variables but does not imply causation. Observing that chirps increase with temperature suggests correlation, but further study is needed to confirm if temperature causes the change in chirping.