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2 weeks ago
Maple trees A forester would like to know how big a maple tree might be at age 50 years. She gathers data from some trees that have been cut down, and plots the diameters (in inches) of the trees against their ages (in years). First she makes a linear model. The scatterplot and residuals plot are shown.


a. Describe the association shown in the scatterplot.
b. Do you think the linear model is appropriate? Explain.
c. If she uses this model to try to predict the diameter of a 50-year old maple tree, would you expect that estimate to be fairly accurate, too low, or too high? Explain.

Now she re-expresses the data, using the logarithm of age to try to predict the diameter of the tree. Here are the regression analysis and the residuals plot.

d. Explain why you think this is a better model.
e. Using this model, predict the diameter of a maple tree at age 50 years.
Textbook 

Stats: Modeling the World


Edition: 4th
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2 weeks ago
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a. The association between age of a maple tree and its diameter is moderately strong, positive, and
    curved, not linear.
b. No, the plot of residuals shows an obvious pattern. Trees with diameters less than 6 inches have
    negative residuals, trees with diameters between 9 and 14 inches have positive residuals, and
    trees with diameters larger than 15 inches have negative residuals.
c. Using this model to predict the diameter of a 50-year old maple tree would be too high. The
    model in the original scatterplot is above the data points in the region of 50 years and the
    residuals above 15 inches are negative indicating that the model would overestimate the
    diameter of the tree.
d. There is no obvious pattern to the residual plot.
e. Model: = -8.6077 + 15.0701[log(Age)]
    At 50 years, = -8.6077 + 15.0701[log(50)] ≈ 17.0
    Prediction for the diameter of a maple tree at age 50 years is 17.0 inches.
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