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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

The scatterplot shows the relationship between the number of people per television set and the number of people per physician for 40 countries, along with the least-squares regression line. In Ethiopia, there were 503 people per TV and 36,660 people per doctor. Which of the following is correct?

a. Increasing the number of TVs in a country will attract more doctors.

b. The slope of the least-squares regression line is less than 1.

c. The correlation is greater than 1.

d. The point for Ethiopia is decreasing the slope of the least-squares regression line.

e. Ethiopia has more people per doctor than expected, based on how many people it has per TV.

Residual gas Refer to Exercise 38. During March, the average temperature was 46.4掳F and Joan used an average of 490 cubic feet of gas per day. Calculate and interpret the residual for this month.

Drilling down beneath a lake in Alaska yields chemical evidence of past changes in climate. Biological silicon, left by the skeletons of single-celled creatures called diatoms, is a measure of the abundance of life in the lake. A rather complex variable based on the ratio of certain isotopes relative to ocean water gives an indirect measure of moisture, mostly from snow. As we drill down, we look further into the past. Here is a scatterplot of data from 2300 to 12,000 years ago:

a. Identify the unusual point in the scatterplot and estimate its x and y coordinates.

b. Describe the effect this point has on

i. the correlation.

ii. the slope and y-intercept of the least-squares line.

iii. the standard deviation of the residuals.

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

use.

d. Interpret the values of s and r2.

More mess? When Mentos are dropped into a newly opened bottle of Diet

Coke, carbon dioxide is released from the Diet Coke very rapidly, causing the Diet Coke to be expelled from the bottle. To see if using more Mentos causes more Diet Coke to be expelled, Brittany and Allie used twenty-four 2-cup bottles of Diet Coke and randomly assigned each bottle to receive either 2, 3, 4, or 5 Mentos. After waiting for the fizzing to stop, they measured the amount expelled (in cups) by subtracting the amount remaining from the original amount in the bottle.29 Here is some computer output from a regression of y = amount expelled on x = number of Mentos:

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 use.

d. Interpret the values of s and r2.

More crying? Refer to Exercise 16Does the fact that r=0.45 suggest that making an infant cry will increase his or her IQ later in life? Explain your reasoning.
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