Question

Measuring tree height is not an easy task. How well does trunk diameter predict tree height? A survey of 958 live trees in an old-growth forest in Canada provides us with the following information: The mean tree height is 15.6 meters (m), with standard deviation 13.4 m; the mean diameter, measured at "breast height" (1.3 m above ground), is 23.4 centimeters (cm), and the standard deviation is 23.5 cm. The correlation between the height and the diameter is very high:

r=0.96
What are the slope and intercept of the regression line to predict tree height from trunk diameter?

Answer 1

The slope of the regression line to predict tree height from trunk diameter is approximately 0.553, and the intercept is approximately 7.366.

Step-by-step explanation:

To find the slope and intercept of the regression line to predict tree height from trunk diameter, we can use the formula: y = mx + b, where y is the dependent variable (tree height), x is the independent variable (trunk diameter), m is the slope, and b is the intercept.

Given that the correlation between the height and the diameter is very high (r = 0.96), the slope of the regression line is equal to the correlation coefficient multiplied by the standard deviation of the dependent variable (tree height) divided by the standard deviation of the independent variable (trunk diameter). Therefore, the slope is: slope = r * (standard deviation of height / standard deviation of diameter).

Plugging in the values given in the question, we have: slope = 0.96 * (13.4 / 23.5).

Finally, we can find the intercept by substituting the slope and the mean values of the independent and dependent variables into the formula: intercept = mean of height - (slope * mean of diameter).

Using the given values, the slope is approximately 0.553 and the intercept is approximately 7.366.