An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree.

Which of the following is the best interpretation of the slope of the regression line?

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The slope of the regression line corresponds to the coefficient next to age. More generally, for a line,

$$ \hat{y}=a + b(x) $$

\(b\) corresponds to the slope of the equation. The slope is the change in \(\hat{y}\) for every change in \(x\).

$$ 0.48=\frac{0.48}{1} = \frac{\text{Change in }\hat{y}}{\text{Change in } x} = \frac{\text{Change in height}}{\text{change in age}} $$