Question: Predicting heights of spruce trees. In forestry, the diameter of a tree at breast height (which is fairly easy to measure) is used to predict the height of the tree (a difficult measurement to obtain). Silviculturists working in British Columbia's boreal forest conducted a series of spacing trials to predict the heights of several species of trees. The data in the next table are the breast height diameters (in centimeters) and heights (in meters) for a sample of 36 white spruce trees.
(a) Construct a scatterplot for the data.
(b) Assuming the relationship between the variables is best described by a straight line, use the method of least squares to estimate the y-intercept and slope of the line.
(c) Plot the least squares line on your scatterplot.
(d) Do the data provide sufficient evidence to indicate that the breast height diameter x contributes information for the prediction of tree height y? Test using α = .05.
(e) Use your least squares line to find a 90% con- fidence interval for the average height of white spruce trees with a breast height diameter of 20 cm. Interpret the interval.