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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset Vaia Explanations$ Math

4th Edition · 809 pages

ISBN: 9781319113339

Chapter 12: Q. 1 (page 759)

Oil and residuals Exercise 59 on page 193 (Chapter 3) examined data on the depth of small defects in the Trans-Alaska Oil Pipeline. Researchers compared the results of measurements on 100 defects made in the field with measurements of the same defects made in the laboratory. The figure below shows a residual plot for the least-squares regression line based on these data. Are the conditions for performing inference about the slope $β$ of the population regression line met? Justify your answer.

Short Answer

Expert verified

The equal variance requirement has not been met.

Step by step solution

01

Given Information

Need to find which variance requirements have not been met.

02

Explanation

There are five conditions for regression inference are: Linear, Independent, Normal, Equal variance, Random

The Equal variance requirement has not been met, because the vertical spread is larger to the right than it is to the left in the residual plot.

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Most popular questions from this chapter

SAT Math scores In Chapter 3, we examined data on the percent of high school graduates in each state who took the SAT and the state's mean SAT Math score in a recent year. The figure below shows a residual plot for the least-squares regression line based on these data. Are the conditions for performing inference about the slope $β$ of the population regression line met? Justify your answer.

Western lowland gorillas, whose main habitat is the central African continent, have a mean weight of $275 p o u n d s$ with a standard deviation of $40 p o u n d s$ . Capuchin monkeys, whose main habitat is Brazil and a few other parts of Latin America, have a mean weight of $6 p o u n d s$ with a standard deviation of $1.1 p o u n d s$ . Both weight distributions are approximately Normally distributed. If a particular western lowland gorilla is known to weigh $345 p o u n d s$ , approximately how much would a capuchin monkey have to weigh, in pounds, to have the same standardized weight as the lowland gorilla?

(a) $4.08$

(b) $7.27$

(c) $7.93$

(d) $8.20$

(e) There is not enough information to determine the weight of a capuchin monkey.

In physics class, the intensity of a 100-watt light bulb was measured by a sensor at various distances from the light source. A scatterplot of the data is shown below. Note that a candela (cd) is a unit of luminous intensity in the International System of Unit

Physics textbooks suggest that the relationship between light intensity y and distance x should follow an “inverse square law,” that is, a power-law model of the form $y = a x^{- 2}$ . We transformed the distance measurements by squaring them and then taking their reciprocals. Some computer output and a residual plot from a least-squares regression analysis on the transformed data are shown below. Note that the horizontal axis on the residual plot displays predicted light intensity

(a) Did this transformation achieve linearity? Give appropriate evidence to justify your answer.

(b) What would you predict for the intensity of a $100$ -watt bulb at a distance of $2.1$ meters? Show your work.

Use this linear model to predict the U.S. population in $1890$ . Show your work.

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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