Introduction It is thought that the size of a plants seed may have some effect on the geographic range of a plant. In fact, a positive correlation is believed to exist between acorn size and the geographical range of the North American Oaks. The idea behind this theory is that larger acorns will be carried away by larger animals who in turn have a wider territorial range. Aizen and Patterson studied 39 species of oak trees to examine this correlation. Protocol Fifty species of oaks are found growing in the United States, 80% of which are accounted for in the Atlantic and California regions. The 28 oaks in the Atlantic region and the 11 oaks in the California region were used in this study. Acorn size was expressed as a volume, using measurements of specific nut lengths and widths to estimate the acorn volume as the volume of an ellipsoid. The area of the geographical range for each species were obtained from the available literature. Results The range of species number 11 of the California region is unusual in that it does not include any land on the continental United States. This particular species of oak grows only on the Channel Islands of Southern California (see map) and the island of Guadalupe off the coast of Baja California. The area of the Channel Islands is 1014 sq. km and the area of the island of Guadalupe is 265 sq. km. The data collected by Aizen and Patterson is given in the table below. The variables in the data table are: Region (Atlantic or California) Range = the geographic area covered by the species in km?x100 Acorn size (cm?) Tree height (m) Species Range Area Acorn Size Tree Height (km2x100) (cm3) (m) Atlantic Region 1 Quercus alba L. 24196 1.4 27 2 Quercus bicolor Willd. 7900 1.4 21 3 Quercus macrocarpa Michx. 23038 9.1 25 4 Quercus prinoides Willd. 17042 1.6 3 5 Quercus Prinus L. 7646 10.5 24 6 Quercus stellata Wang. 19938 2.5 17 7 Quercus virginiana Mill 7985 0.9 15 8 Quercus Michauxii Nutt. 8897 6.8 30 9 Quercus lyrata Walt. 8982 1.8 24 10 Quercus Laceyi Small. 233 0.3 11 11 Quercus Chapmanii Sarg. 1598 0.9 15 12 Quercus Durandii Buckl. 1745 0.8 23 13 Quercus Muehlenbergii Engelm 17042 2.0 24 14 Quercus ilicifolia Wang. 4082 1.1 3 15 Quercus incana Bartr. 3775 0.6 13 16 Quercus falcata Michx. 13688 1.8 30 17 Quercus laevis Walt. 3978 4.8 9 18 Quercus laurifolia Michx. 5328 1.1 27 19 Quercus marilandica Muenchh. 18480 3.6 9 20 Quercus nigra L. 10161 1.1 24 21 Quercus palustris Muenchh. 8643 1.1 23 22 Quercus Phellos L. 9920 3.6 27 23 Quercus rubra L. 28389 8.1 24 24 Quercus velutina Lam. 21067 3.6 23 25 Quercus imbricaria Michx. 14870 1.8 18 26 Quercus myrtifolia Willd. 2540 0.4 9 27 Quercus texana Buckl. 829 1.1 9 28 Quercus coccinea Muenchh. 8992 1.2 4 California Region 1 Quercus Douglasii Hook. & Arn 559 4.1 18 2 Quercus dumosa Nutt. 433 1.6 6 3 Quercus Engelmannii Greene 259 2.0 17 4 Quercus Garryana Hook. 1061 5.5 20 5 Quercus lobata Nee 870 5.9 30 6 Quercus agrifolia Nee. 803 2.6 23 7 Quercus Kelloggii Newb. 826 6.0 26 8 Quercus Wislizenii A. DC. 699 1.0 21 9 Quercus chrysolepis Liebm. 690 17.1 15 10 Quercus vaccinifolia Engelm. 233 0.4 1 11 Quercus tomentella Engelm 13 7.1 18 Questions Make a scatter plot of tree range vs. acorn size. What is the correlation? Does there appear to be any linear relationship between range and acorn size? Examine the summary statistics for tree range. What are the mean and the standard deviation? What do these values tell you about the likely shape of the distribution? Now regress Range on Acorn size. If you want to be able to predict tree range by knowing acorn size, how much does this regression equation help you? Explain. Examine a normal probability plot of tree range and a normal probability plot of acorn size. Do these data appear to follow a normal distribution? If not, what shape do they have? You may wish to look at the histogram of the variables. Transform the data using the log transformation on both the range and the size. Now make a scatter plot of Ln(range) vs. Ln(acorn size). How did the correlation change? Does the correlation surprise you? Do you see any obvious reason that might help explain the correlation? Examine the normal probability plots of Ln(range) and Ln(acorn size). What do they tell you? Make a scatter plot of Ln(range) vs. Ln(acorn size) for the Atlantic region. Is the correlation any better than that found in Question 5? Make a scatter plot of Ln(range) vs. Ln(acorn size) for the California region. What is the correlation? Why do you think that the correlation is so low? Examine the residuals from the regression of Ln(range) on Ln(acorn size) and the indicator for region. Does there seem to be an outlier? Can you identify the outlier? b) What is unusual about the species of oak represented by this outlier? (Hint: Consult themap of the region.) How does this information help you understand this data point and explain the outlier?
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