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Chapter 12: Q.40 (page 789)

Determining tree biomass It is easy to measure the 鈥渄iameter at breast height鈥� of a tree. It鈥檚 hard to measure the total 鈥渁boveground biomass鈥� of a tree, because to do this you must cut and weigh the tree. The biomass is important for studies of ecology, so ecologists commonly estimate it using a power model. Combining data on 378trees in tropical rain forests gives this relationship between biomass y measured in kilograms and diameter x measured in centimeters:

lny^=-2.00+2.42lnx

Short Answer

Expert verified

The biomass of a tropical tree 30centimeters in diameter

isy^=508.213.

Step by step solution

01

Given Information

Given in the question that,

lny^=-2.00+2.42lnx.

02

Explanation

we must calculate the biomass of a tropical tree with a diameter of 30centimeters. As a result, we'll rate the model as follows:

lny^=-2.00+2.42lnx

鈬�lny^=-2.00+2.42ln(30)

鈬�lny^=6.23090

localid="1651133502568" 鈬�y^=e6.23090

=508.213

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Most popular questions from this chapter

The swinging pendulum Mrs. Hanrahan鈥檚 precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-and-forth swing (called its period). Here are their data:

(a) Make a reasonably accurate scatterplot of the data by hand, using length as the explanatory variable. Describe what you see. (b) The theoretical relationship between a pendulum鈥檚 length and its period is

period=2蟺glength

where gis a constant representing the acceleration due to gravity (in this case, g=980cm/s2). Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).

(c) Use the following graph to identify the transformation that was used to linearize the curved pattern in part (a).

Random assignment is part of a well-designed comparative experiment because

(a) It is more fair to the subjects.

(b) It helps create roughly equivalent groups before treatments are imposed on the subjects.

(c) It allows researchers to generalize the results of their experiment to a larger population.

(d) It helps eliminate any possibility of bias in the experiment.

(e) It prevents the placebo effect from occurring

Is there significant evidence that selling price increases as appraised value increases? To answer this question, test the hypotheses

(a) H0:尾=0versusHa:尾>0..

(b) H0:尾=0versusHa:尾<0

(c) H0:尾=0versusHa:尾鈮�0

(d) H0:尾>0versusHa=尾=0.

(e)Hx:尾=1versus.H路胃>1

6. Beer and BAC Refer to Exercise 4. Computer output from the least-squares regression analysis on the beer and blood alcohol data is shown below.


The model for regression inference has three parameters:伪,尾and蟽Explain what each parameter represents in context. Then provide an estimate for each.

Prey attracts predators Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. The researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He chose young perch at random from a large group and placed 10,20,40 and60 perch in the four pens. Then he dropped the nets protecting the pens, allowing the bass to swarm in, and counted the perch left after two hours. Here are data on the proportions of perch eaten in four repetitions of this setup .

The explanatory variable is the number of perch (the prey) in a confined area. The response variable is the proportion of perch killed by bass (the predator) in two hours when the bass are allowed access to the perch. A scatterplot of the data shows a linear relationship.

We used Minitab software to carry out a least-squares regression analysis for these data. A residual plot and a histogram of the residuals are shown below. Check whether the conditions for performing inference about the regression model are met.
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