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Chapter 3: Q 61. (page 194)

Nahya infant weights A study of nutrition in developing countries collected data from the Egyptian

village of Nahya. Here are the mean weights (in kilograms) for 170 infants in Nahya who were

weighed 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 plotting the data. The result is weight=4.88+0.267(age) A residual plot is shown below. Would it be appropriate to use this regression line to predict y from x? Justify your answer.

Short Answer

Expert verified

A straight line is not an appropriate model for these data.

Step by step solution

01

Given information

weight =4.88+0.267(age)

Age123456789101112
Weight4.35.15.76.36.87.17.27.27.27.27.57.8
02

Concept

Linear regression is commonly used for predictive analysis and modeling.

03

Calculation

Without displaying the data, a quick statistician enters the data into software and computes the least square line.

The result is weight=4.88+0.2670.05762(age)

The shown residual graphic effectively horizontalizes the regression line. It amplifies the points' deviations from the line; if the regression line reflects the main pattern of the data, the residuals should be devoid of pattern. A residual plot with a visible curved pattern is seen in the image above. For these data, a straight line is not an effective model.

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Most popular questions from this chapter

A recent study discovered the correlation between the age at which an infant first speaks and the child’s score on an IQ test given upon entering elementary school is −0.68. A scatterplot of the data shows a linear form. Which of the following statements about this finding is correct?

(a) Infants who speak at very early ages will have higher IQ scores by the beginning of elementary school than those who begin to speak later.

(b) 68%of the variation in IQ test scores is explained by the least-squares regression of age at first spoken word and IQ score.

(c) Encouraging infants to speak before they are ready can have a detrimental effect later in life, as evidenced by their lower IQ scores.

(d) There is a moderately strong, negative linear relationship between age at first spoken word and later IQ test scores for the individuals in this study.

You use the same bar of soap to shower each morning. The bar weighs 80grams when it is new. Its weight goes down by 6 grams per day on average. What is the equation of the regression line for predicting weight from days of use?

All brawn? The figure below plots the average brain weight in grams versus average body weight in kilograms for 96species of mammals. There are many small mammals whose points at the lower-left overlap.

(a) The correlation between body weight and brain weight isr=0.86. Explain what this value means.

(b) What effect would removing the elephant have on the correlation? Justify your answer.

The scatterplots below show four sets of real data:

(a) repeats the manatee plot in Figures

(b) shows the number of named tropical storms and the number predicted before the start of hurricane season each year between 1984and 2007by William Gray of Colorado State University;

(c) plots the healing rate in micrometers (millionths of a meter) per hour for the two front limbs of several newts in an experiment; and

(d) shows stock market performance in consecutive years over a 56-year period.

For each graph, estimate the correlation r. Then interpret the value of r in context.

(a)

(b)

(c)

(d)

A school guidance counselor examines the number of extracurricular activities that students do and their grade point average. "The evidence suggests that the association between the number of extracurricular activities a kid participates in and his or her grade point average is close to zero," the guidance counsellor explains.” A correct interpretation of this statement would be that

(a) active students tend to be students with poor grades, and vice versa.

(b) students with good grades tend to be students who are not involved in many extracurricular activities, and vice versa.

(c) students involved in many extracurricular activities are just as likely to get good grades as bad grades; the same is true for students involved in few extracurricular activities.

(d) there is no linear relationship between a number of activities and grade point average for students at this school.

(e) involvement in many extracurricular activities and good grades go hand in hand.
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