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Chapter 4: Q. 4.69 (page 175)

Wasp Mating Systems. In the paper "Mating System and Sex Allocation in the Gregarious Parasitoid Cotesia glomerata" (Animal Behaviour, Vol. 66, pp. 259-264). H. Gu and S. Dorn reported on various aspects of the mating system and sex allocation strategy of the wasp C. glomerata, One part of the study involved the investigation of the percentage of male wasps dispersing before mating in relation to the brood sex ratio (proportion of males). The data obtained by the researchers are on the WeissStats site.

a. Obtain a scatterplot for the data.

b. Is it reasonable to find a regression line for the data? Explain your answer.

Short Answer

Expert verified

a. The graph of scatterplot is as,

b. It is not reasonable to find a regression line for the data.

Step by step solution

01

Part (a) Step 1: Given Information

One part of the study involved the investigation of the percentage of male wasps dispersing before mating in relation to the brood sex ratio (proportion of males). The data obtained by the researchers are on the Weiss Stats site.

02

Part (a) Step 2: Explanation 

MINITAB can be used to create a scatterplot using the provided data:

Step 1: Choose Graph>Scatterplot

Step 2: Choose With Connect Line, and then click OK.

Step 3: Under Yvariables, enter a column of %DISPERSING

Step 4: Under Xvariables, enter a column of SEX RATIO

Step 5: Click OK

The scatterplot is as,

03

Part (b) Step 1: Given Information

To determine whether or not finding a regression line is reasonable.

04

Part (b) Step 2: Explanation 

As the observation points are scattered around the curve, finding a regression line does not make sense since there is no linear pattern in the points.

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Most popular questions from this chapter

Tine Series. A collection of observations of a variable y taken at regular intervals over time is called a time series. Bocoomsic data and electrical signals are examples of time series. We can think of a time series as providing data points x1+y2where x0is the ith observation time and yiis the observed value of y at time xi. If a time series exhibits a linear trend, we can find that trend by determining the regression equation for the data points. We can then use the regression equation for forecasting purposes.

As an illustration, consider the data on the WeissStats site that shows the U.S. population, in millions of persons, for the years 1900 2013. as provided by the I.S. Census Beret.

a. Use the technology of your choice to lesbian a scatterplot of the data.

h. Use the technology of your choice to find the regression equation.

6. Use your result from part (b) to forecast the U.S. population for the years 2014 and 2015 .

(a) Plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.

(b) Construct tables forx,y,e,e2,y^

(c) Determine which line fits the data points better according to the least-square criterion.

4.78 Gas Guzzlers. The magazine Consumer Reports publishes information on automobile gas mileage and variables that affect gas mileage. In one issue, data on gas mileage (in miles per gallon) and engine displacement (in liters) were published for 121vehicles. Those data are available on the Weiss Stats site.

a. Obtain a scatterplot for the data.

b. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c) (f).

(a) Plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.

(b) Construct tables for x,y,e,e2,y^

(c) Determine which line fits the data points better according to the least-square criterion.

13. Identify a use of the coefficient of determination as a descriptive measure.
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