The following table gives data on the mean number of seeds produced in a year by several common tree species and the mean weight (in milligrams) of the seeds produced. Two species appear twice because their seeds were counted in two locations. We might expect that trees with heavy seeds produce fewer of them, but what mathematical model best describes the relationship?28 Tree species Seed count Seed weight (mg)

Paper birch 27,239 0.6 Yellow birch 12,158 1.6 White spruce 7202 2.0 Engelmann spruce 3671 3.3 Red spruce 5051 3.4 Tulip tree 13,509 9.1 Ponderosa pine 2667 37.7 White fir 5196 40.0 Sugar maple 1751 48.0 Sugar pine 1159 216 American beech 463 247 American beech 1892 247 Black oak 93 1851 Scarlet oak 525 1930 Red oak 411 2475 Red oak 253 2475 Pignut hickory 40 3423 White oak 184 3669 Chestnut oak 107 4535

(a) Based on the scatterplot below, is a linear model appropriate to describe the relationship between seed count and seed weight? Explain.

(b) Two alternative models based on transforming the original data are proposed to predict the seed weight from the seed count. Graphs and computer output from a least-squares regression analysis on the transformed data are shown below.

Predictor Coef SE Coef T P Constant 6.1394 0.5726 10.72 0.000 Seed Count -0.00033869 0.00007187 -4.71 0.000 S = 2.08100 R-Sq = 56.6% R-Sq(adj) = 54.1%

Predictor Coef SE Coef T P Constant 15.491 1.081 14.33 0.000 ln(count) -1.5222 0.1470 -10.35 0.000 S = 1.16932 R-Sq = 86.3% R-Sq(adj) = 85.5%
Which model, A or B, is more appropriate for predicting seed weight from seed count? Justify your answer.

(c) Using the model you chose in part (b), predict the seed weight if the seed count is 3700.

(d) Interpret the value of r2 for your model.

Transcribed Image Text:

Seed weight (mg) 5000 4000 3000 2000 1000 0 0 5000 10,000 15,000 Seed count 20,000 25,000 30,000