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Chapter 3: Q 47. (page 204)

Infant weights in Nahya A study of nutrition in developing countries

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.

Short Answer

Expert verified

No, it is not appropriate.

Step by step solution

01

Given information

The figure is:

02

Concept

The least-squares regression line reduces the sum of squares of vertical distances between the observed points and the line to zero.

03

Explanation

Regression equation is:

weight=4.88+0.267(age)

The data points on the residual plot should follow a linear pattern, which is an important property of an adequate linear regression model. The data points in the provided residual plot do not form linear patterns, making the model incorrect. Simply put, the existence of curvature in the residual plot indicates that the model is ineffective.

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Most popular questions from this chapter

Calculating achievement a study found a strong link between the number of calculators possessed by high school pupils and their arithmetic proficiency, according to the principle of a high school. Based on this study, he decides to buy each student at his school two calculators, hoping to improve their math achievement. Explain the flaw in the principal鈥檚 reasoning.

One child in the Mumbai study had height 59 cm and arm span 60 cm. This child鈥檚 residual is

a. 鈭�3.2 cm.

b. 鈭�2.2 cm.

c. 鈭�1.3 cm.

d. 3.2 cm.

e. 62.2 cm.

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.

a. Is a line an appropriate model to use for these data? Explain how you know.

b. Find the correlation.

c. What is the equation of the least-squares regression line? Define any variables that you

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d. Interpret the values of s and r2.

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a. Is a line an appropriate model to use for these data? Explain how you know.

b. Find the correlation.

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Rank the correlations Consider each of the following relationships: the heights of fathers and the heights of their adult sons, the heights of husbands and the heights of their wives, and the heights of women at age 4 and their heights at age 18. Rank the correlations Page Number: 174between these pairs of variables from largest to smallest. Explain your reasoning.
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