Use the following information for question 5.

Suppose you were to collect weekly data for ice cream cone sales and air conditioner sales. You want to make a scatterplot. Which variable would you use as the explanatory variable, and which as the response variable? Why?

Question

Use the following information for question 5.

Suppose you were to collect weekly data for ice cream cone sales and air conditioner sales. You want to make a scatterplot. Which variable would you use as the explanatory variable, and which as the response variable? Why?

BlackTom AI · Accepted Answer

This question asks about which variable to treat as explanatory versus response when plotting weekly ice cream cone sales and weekly air conditioner sales, with temperature implied as a lurking variable.
Option: 'Neither variable is explanatory. Both are responses to the lurking variable of temperature.'
First, consider what makes a variable explanatory in a scatterplot: it should be the variable that you think is driving or predicting changes in the other variable. In this context, temperature is the underlying factor that influences both ice cream cone sales and air conditioner sales.
Since temperature affects both outcomes, neither ice cream sales nor air conditioner sales alone is the sole predictor of the other. If you were to construct a scatterplot with one of the given variables on the x-axis and the other on the y-axis, you would implicitly be conditioning on a relationship that is actually mediated by temperature, which is not directly included in the plotted data.
Therefore, interpreting either ice cream sales or air conditioner sales as the sole explanatory variable would misrepresent the causal structure, because both are responding to the same underlying temperature changes. This makes the option that neither variable is explanatory and that both are responses to temperature a reasonable characterization of the situation.
A common misconception would be to pick one of the two sales variables as explanatory and the other as the response, which would imply a direct predictive relationship between the two sales figures independent of temperature. In reality, without temperature data, such a direct interpretation would be misleading, since the apparent association could be driven by the lurking variable (temperature).
In summary, given the lurking variable temperature influencing both sales metrics, the most accurate view among the presented choices is that neither ice cream sales nor air conditioner sales should be treated as explanatory for the other; instead both are responses to the same temperature driver.

Use the following information for question 5. Suppose you were to collect weekly data for ice cream cone sales and air conditioner sales. You want to make a scatterplot. Which variable would you use as the explanatory variable, and which as the response variable? Why?Single choice

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