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 13.4m; the mean diameter, measured at “breast height” (1.3 aboveground), is 23.4 centimeters (cm), and the standard deviation is 23.5 cm. The correlation between the height and diameter is very high: r=0.96.

(a) What are the slope and intercept of the regression line to predict tree height from trunk diameter? Draw a graph of this regression line.

(b) The tree diameters ranged from 1 to 101 cm. Predict the height of a tree in this area that is 50 cm in diameter at breast height. Use r2 to assess the reliability of this prediction.