The article "Testing the Influence of Climate, Human Impact and Fire on the Holocene Population Expansion of Fagus sylvatica in the Southern Prealps (Italy)" (V. Valsecchi, W. Flnsinger, et al., The Holocene 2008:603-614) presents calculations of the ages (in calendar years before 1950) of several sediment samples taken at various depths (in cm) in Lago di Fimon, a lake in Italy. The results are presented in the following table.
Depth Age
284.5...................1255
407.5...................3390
512.0...................5560
551.0...................6670
578.5...................7160
697.0...................9820
746.5.................11,030
a. Construct a scatterplot of age (y) versus depth (x). Verify that a linear model is appropriate.
b. Compute the least-squares line for predicting age from depth.
c. If two samples differ by 100 cm in depth, by how much would you predict their ages to differ?
d. Predict the age for a specimen whose depth is 600 cm.
e. Should the least-squares line be used to predict the age for a depth of 50 cm? If so, predict the age. If not, explain why not.
f. For what depth would you predict an age of 5000?