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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

In a scatterplot of the average price of a barrel of oil and the average retail price of a gallon of gas, you expect to see

a. very little association.

b. a weak negative association.

c. a strong negative association.

d. a weak positive association.

e. a strong positive association.

Who’s got hops? Haley, Jeff, and Nathan measured the height (in inches)

and vertical jump (in inches) of 74 students at their school.34 Here is a scatterplot of the data, along with the least-squares regression line. Jacob (highlighted in red) had a vertical jump of nearly 3 feet!

a. Describe the influence that Jacob’s point has on the equation of the least-squares regression line.

b. Describe the influence that Jacob’s point has on the standard deviation of the residuals and r2

Using data from the LPGA tour, a regression analysis was performed using x = average driving distance and y = scoring average. Using the output from the regression analysis shown below, determine the equation of the least-squares regression line.

a. y^=87.974+2.391x

b. y^=87.974+1.01216x

c. y^=87.974−0.060934x

d. y^=−0.060934+1.01216x

e. y^=−0.060934+87.947x

More putting success Refer to your graph from Exercise 4 Describe the relationship between distance from hole and percent of putts made for the sample of professional golfers.

More hot dogs Refer to Exercise 19

a. Explain why it isn’t correct to say that the correlation is 0.87mg/cal

b. What would happen to the correlation if the variables were reversed on the scatterplot? Explain your reasoning.

c. What would happen to the correlation if sodium was measured in grams instead of milligrams? Explain your reasoning.
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