Tree cross-sectional area and timber volume
Use this page to explain that the regression model with β0, β1 and σ replaced by estimates provides an estimate of the response distribution at any new x-value.
The grey band represents the fitted regression line ± twice the estimated standard deviation of the model error. Use the slider to show the estimated normal distribution of the timber volume in trees with any cross-section.
The mean of this estimated distribution (i.e. the prediction from the least squares line) provides a point prediction.
The value of hardwood trees depends on the volume of timber that can be obtained when the trees are harvested. However the volume of timber cannot be easily measured when the tree is standing, so volume is usually estimated from measurements that are easier to make, such as the tree diameter 4.5 feet above ground level. The diagram below plots the cross-sectional area at this height against the volume of timber for 31 black cherry trees that were harvested in the Allegheny National Forest in Pennsylvania.