Q 61. Nahya infant weights A study of ... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

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 $w e i g h t = 4.88 + 0.267 (a g e)$ 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

Given information

weight $= 4.88 + 0.267 (a g e)$

Age	1	2	3	4	5	6	7	8	9	10	11	12
Weight	4.3	5.1	5.7	6.3	6.8	7.1	7.2	7.2	7.2	7.2	7.5	7.8

Concept

Linear regression is commonly used for predictive analysis and modeling.

Calculation

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

The result is $w e i g h t = 4.88 + 0.2670.05762 (a g e)$

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.