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Chapter 3: Q 10. (page 172)

Do muscles burn energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate of 12 women who are subjects in a study on dieting. Lean body mass, given in kilograms, is a person’s weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours. The researchers believe that lean body mass is an

important influence on metabolic rate.

a. Make a scatterplot to display the relationship between lean body mass and metabolic rate.

b. Describe the relationship between lean body mass and metabolic rate.

Short Answer

Expert verified

Part (b) Linear, positive and moderately strong association without outliers.

Part (a)

Step by step solution

01

Part (a) Step 1: Given information

Data on 12 women's lean body mass and resting metabolic rate:

02

Part (a) Step 2: Explanation

For Scatterplot:

On horizontal axis: Lean body mass

On vertical axis: Metabolic rate

03

Part (b) Step 1: Explanation

Strength: The scatterplot's spots do not lie closer together, nor do they sprawl widely away. As a result, the strength will be mild.

Unusual features: Because there are no points in the scatterplot that deviate significantly from the overall pattern. As a result, there are no outliers.

Form: Because there is no substantial curvature in the scatterplot. As a result, the shape will be linear.

Direction: Because the scatterplot's pattern is upwards sloping. As a result, the trend will be positive.

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Most popular questions from this chapter

Dem bones Archaeopteryx is an extinct beast that had feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil specimens are known to exist today. Because these specimens differ greatly in size, some scientists think they are different species rather than individuals from the same species. If the specimens belong to the same species and differ in size because some are younger than others, there should be a positive linear relationship between the lengths of a pair of bones from all individuals. An outlier from

this relationship would suggest a different species. Here are data on the lengths (in centimeters) of the femur (a leg bone) and the humerus (a bone in the upper arm) for the five specimens that preserve both bones:

a. Make a scatterplot. Do you think that all five specimens come from the same species? Explain.

b. Find the correlation r step by step, using the formula on page 166. Explain how your value for r matches your graph in part (a).

Actual consumption Refer to Exercise 48. Use the equation of the least-squares regression line and the residual plot to estimate the actual fuel consumption of the car when driving 20 kilometers per hour.

Suppose that a tall child with an arm span of 120 cm and a height of 118 cm was added to the sample used in this study. What effect will this addition have on the correlation and the slope of the least-squares regression line?

a. Correlation will increase, and the slope will increase.

b. Correlation will increase, and the slope will stay the same.

c. Correlation will increase, and the slope will decrease.

d. Correlation will stay the same, and the slope will stay the same.

e. Correlation will stay the same, and the slope will increase.

The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable x to be the percent change in a stock market index in January and the response variable y to be the change in the index for the entire year. We expect a positive correlation between x and y because the change during January contributes to the full year’s change. Calculation from data for an 18-year period gives x = X=1.75%sx=5.36%y=9.07%sy=15.35%r=0.596

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(b) The mean change in January is x=1.75%. Use your regression line to predict the change in the index in a year in which the index rises1.75% in January. Why could you have given this result (up to roundoff error) without doing the calculation?

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collected data from the Egyptian village of Nahyan. Researchers recorded the mean weight (in kilograms) for 170 infants in Nahya each month during their first year of life. A hasty user of statistics enters the data into software and computes the least-squares line without looking at the scatterplot first. The result is weight^=4.88+0.267 (age). Use the residual plot to determine if this linear model is appropriate.

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