Regression Since regression is such a widely used statistical method lets revisit the topic now that we have statistical inference tools. We will use confidence intervals and hypothesis tests to determine if the relationship between two quantitative variables has occurred by chance alone. Any ideas on how she might do this? She hopes predicting volume of wood from tree diameter for individual trees will help determine total volume for the piece of forest land. She investigates, "Can the volume of wood for a tree be predicted by its diameter?" First she randomly samples 31 trees and measures the diameter of each tree and then its volume. Is the relationship linear? Now we compute the slope and the intercept for least squares regression line. What would happen if the forest service agent took another sample of 31 trees? Would the slope change? Would the intercept change? What about a third sample of 31 trees?