Improving trees In the last exercise you saw that the linear model had some deficiencies. Lets create a better model. a) Perhaps the cross-sectional area of a tree would be a better predictor of its age. Since area is measured in square units, try re-expressing the data by squaring the diameters. Does the scatterplot look better? b) Create a model that predicts Age from the square of the Diameter. c) Check the residuals plot for this new model. Is this model more appropriate? Why? d) Estimate the age of a tree 18 inches in diameter.

Chapter 5 --- Randomness and Probability Spin a penny example in class: What is the probability of a headWhy Why is it calledan empirical probability Are spins independent If the first 10 spins are heads is the 11 spin more likely or less likely to be a head What does the “Law of Averages” say How does the Law of LargeNumbersapply to spinning pennies Random Predictability If time permits we will draw some random samples using a Red Bead box. The box is filled with white, red and black beads. We will drawrandom samples of 50 beads from the box and count the number of colored (red or black) beads. Each sample is random and we can’t predict how many colored beads there will be in the next sample. However we can predict a pattern