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Chapter 12: Q. 45 (page 791)

Suppose that the relationship between a response variable y and an explanatory variable x is modelled by y=2.7(0.316)x. Which of the following scatterplots would approximately follow a straight line?

(a) A plot of y against x

(b) A plot of y against log x

(c) A plot of log y against x

(d) A plot of log y against log x

(e) None of (a) through (d)

Short Answer

Expert verified

The scatterplots that approximately follow a straight line is option (c) A plot of log y against x.

Step by step solution

01

Given information

The relationship between a response variable y and an explanatory variable x is modelled byy=2.7(0.316)x.

02

Explanation

The given equation is

y=2.7(0.316)x

The scatterplot will not be a straight line since this equation represents an exponential function, which is not linear.

If we multiply both sides of the equation by the logarithm, we get:

logy=log2.7(0.316)x=log2.7+log0.316x=log2.7+xlog0.316

This is a linear equation with variables log yand xand thus the scatterplot will be a straight line in this case.

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Most popular questions from this chapter

Beavers and beetles Do beavers benefit beetles? Researchers laid out 23 circular plots, every four meters in diameter, at random in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth so beetles prefer them. If so, more stumps should produce more beetle larvae.

Minitab output for a regression analysis on these data is shown below. Construct and interpret a 99% confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met.

The school board in a certain school district obtained a random sample of 200residents and asked if they were in favor of raising property taxes to fund the hiring of more statistics teachers. The resulting confidence interval. for the true proportion of residents in favor of raising taxes was (0.183,0.257). The margin of error for this confidence interval is

(a) 0.037

(b) 0.183

c) 0.220

(d) 0.257

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A 95%confidence interval for the population slope βis

(a) 1.0466±149.5706.

(b) 1.0466±0.2415.

(c) 1.0466±0.2387.

(d) 1.0466±0.1983.

(e) 1.0466±0.1126.

Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If you have studied physics, then you probably know that the theoretical relationship between the variables is distance=490(time)2. A scatterplot of the students’ data showed a clear curved pattern. A scatterplot of which of the following should have a roughly linear pattern?

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Beavers and beetles Refer to Exercise 9.

(a) How many clusters of beetle larvae would you predict in a circular plot with 5 tree stumps cut by beavers? Show your work.

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