Concept explainers
Femur Length and Height Anthropologists use a linear model that relates femur length to height. The model allows an anthropologist to determine the height of an individual when only a partial skeleton (including the femur) is found. In this problem we find the model by analyzing the data on femur length and height for the eight males given in the table.
- (a) Make a scatter plot of the data.
- (b) Find and graph a linear function that models the data.
- (c) An anthropologist finds a femur of length 58 cm. How tall was the person?
Femur length (cm) | Height (cm) |
50.1 | 178.5 |
48.3 | 173.6 |
45.2 | 164.8 |
44.7 | 163.7 |
44.5 | 168.3 |
42.7 | 165.0 |
39.5 | 155.4 |
38.0 | 155.8 |
(a)
To graph: The scatter plot of the data.
Explanation of Solution
Graph:
Consider the femur length as the x coordinates and height as the y coordinates.
The scatter plots of the given data are shown below in Figure 1.
In Figure 1, all the points are plotted on the graph. No two points coincide each other.
(b)
To find: The linear function that represents the given data and draw the graph for it.
Answer to Problem 1P
The linear function that represents the given data is
Explanation of Solution
By the use of online calculator, the regression line for the given data obtained is
The above regression line is in the form of linear equation.
Therefore, the linear function that represents the given data is
The graph that represents the equation
From Figure 2, the graph for the linear equation
(c)
To find: The height of the person if the femur length is 58 cm.
Answer to Problem 1P
The height of the person if the femur length is 58 cm is 191.748 cm.
Explanation of Solution
Consider the length of the femur is 58 cm.
From part (b), it is obtained that the linear equation that represents the given data is
Substitute x = 58 in the above equation to compute the height.
Thus, the height of the person if the femur length is 58 cm is 191.748 cm.
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning