Which of the following values represents the predicted change in the height of the tree for each one-meter increase in the diameter of the tree?
Understand the Problem
The question is asking for the predicted change in the height of a tree based on an increase in the diameter of the tree, using regression analysis output.
Answer
$30$
Answer for screen readers
The predicted change in height of the tree for each one-meter increase in diameter is $30$ meters.
Steps to Solve
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Understanding Regression Output The regression output provides estimates for the intercept and slope (which is the coefficient for the diameter). The slope indicates how much the height of the tree is expected to change for each one-meter increase in the diameter.
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Identify the Slope for Diameter From the output, we see the "Estimate" for the "Diameter" variable is 30. This means that for each 1-meter increase in diameter, the height of the tree is predicted to increase by 30 meters.
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Conclude the Predicted Change Thus, the predicted change in height for each one-meter increase in diameter is 30.
The predicted change in height of the tree for each one-meter increase in diameter is $30$ meters.
More Information
This value indicates a strong positive relationship between the diameter of the tree and its height, suggesting that as trees grow in trunk diameter, their height increases significantly.
Tips
- Confusing the intercept with the slope. The intercept value does not represent the change per unit increase; it is simply the height when the diameter is zero.
- Misreading the coefficient for diameter, which can lead to incorrect conclusions about the height increase.
