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1. The height (in feet) and volume of usable lumber (in cubic feet) of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree. The results are plotted below.

(a) In this study, the response variable (y) is

 A. volume.

 B. height.

 C. neither height nor volume. The measuring instrument used to measure height is the response variable.

 D. height or volume. It doesn't matter which is considered the response.

The response variable in a study refers to the outcome or dependent variable, which is what you're trying to predict or explain. In this case, the researcher is attempting to estimate the **volume of usable lumber** based on the **height** of the tree. Therefore, the response variable is the **volume**.

The predictor or explanatory variable is the **height**, as it is being used to estimate the volume.

Thus, the correct answer is:
**A. Volume**

Would you like further details on this or have any additional questions?

Here are 5 related questions to deepen your understanding:
1. What is the predictor variable in this scenario?
2. How can a regression model help in predicting the volume based on the height?
3. What are some methods to evaluate the accuracy of the regression model in this case?
4. How would you describe the relationship between height and volume based on the scatter plot?
5. Could the relationship between height and volume be non-linear? How would you check this?

**Tip:** Always ensure to label your response and predictor variables correctly when setting up any regression analysis.

The height (in feet) and volume of usable lumber (in cubic feet) of 32 cherry trees are measured by a researcher. The goal is to determine if the volume of usable lumber can be estimated from the height of a tree. The results are plotted in a scatter plot.

Explore how to estimate the volume of usable lumber from tree height using regression analysis. This study measures the height and volume of 32 cherry trees, with results shown in a scatter plot. Learn key concepts like linear regression and how the least squares method is applied. Suitable for high school students in Grades 9-12.

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