"In Exercises 9 and 10, identify the explanatory variable and the response variable.
9. A nutritionist wants to determine whether the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight
loss."

Verified step by step guidance

1. Step 1: Understand the problem by identifying the two variables involved. The problem mentions 'amounts of water consumed each day' and 'individual weight loss.' These are the two variables we need to classify as explanatory and response variables.
2. Step 2: Recall the definitions of explanatory and response variables. The explanatory variable is the one that is manipulated or used to explain changes in another variable, while the response variable is the outcome or the variable being measured.
3. Step 3: Analyze the relationship described in the problem. The nutritionist wants to determine if the 'amounts of water consumed each day' can be used to predict 'individual weight loss.' This suggests that the 'amounts of water consumed each day' is the variable being used to explain or predict changes in 'individual weight loss.'
4. Step 4: Assign the explanatory and response variables based on the analysis. The 'amounts of water consumed each day' is the explanatory variable because it is used to predict, and 'individual weight loss' is the response variable because it is the outcome being measured.
5. Step 5: Conclude that the explanatory variable is 'amounts of water consumed each day,' and the response variable is 'individual weight loss.' This classification helps in understanding the relationship being studied in the problem.

Key Concepts

Explanatory Variable

The explanatory variable, also known as the independent variable, is the factor that is manipulated or categorized to observe its effect on another variable. In the context of the question, it refers to the amount of water consumed each day, as this is the variable the nutritionist is examining to see how it influences weight loss.

Response Variable

The response variable, or dependent variable, is the outcome that is measured to assess the effect of the explanatory variable. In this scenario, the response variable is individual weight loss, as it is the result that the nutritionist aims to predict based on the amount of water consumed.

Causation vs. Correlation

Understanding the difference between causation and correlation is crucial in statistics. Causation implies that changes in the explanatory variable directly cause changes in the response variable, while correlation indicates a relationship without implying direct influence. The nutritionist's study seeks to explore whether water consumption can causally affect weight loss, which requires careful analysis to establish.