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Anthropologists use a linear model that relates human femur (thighbone) 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. Here we find the model by analyzing the data on femur length and height for the eight males given in the following table.
(a) Make a scatter plot of the data.(b) Find and graph the regression line that models the data.(c) An anthropologist finds a human femur of length 53 cm. How tall was the person?
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01:22
Clarissa Noh
Calculus 1 / AB
Calculus 2 / BC
Calculus 3
Chapter 1
Functions and Models
Section 2
Mathematical Models: A Catalog of Essential Functions
Functions
Integration Techniques
Partial Derivatives
Functions of Several Variables
Tilahun J.
September 17, 2022
Then use the regression equation to find the height of a person for a metacarpal length of 44 cm and for a metacarpal length of 55 cm. ?Which height that you calculated do you think is closer to the true height of the person? Why?
Johns Hopkins University
Oregon State University
Baylor University
University of Michigan - Ann Arbor
Lectures
04:31
A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
12:15
In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.
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in this problem. We're looking at the relationship between femur length and height in humans and were given a bunch of data, and we want to make a scatter plot. So using a graphing calculator, the first thing we want to do is go into the stat menu and then into edit, and we can type our numbers into list one and list, too. The next thing we want to do is go into the stat plot menu, which is second y equals Go into menu for staff plot number one and turn it on and make sure that it's a scatter plot using list one and list, too. Once we have those settings, we can go into the zoom menu and choose Zoom nine, which is, um, stat. So here we see our scatter plot. You could imagine that this is roughly linear, although it's not really great, but it looks somewhat linear. We have some clusters. So for Part B, we want to find an graph the regression line that models the data so we can use the calculator for that as well go back into the stat menu and over to the calculate option, go down to number four Linear regression and press enter. We are using list one and list to We don't need to worry about frequency list. And because we do want to graph the line, we're going to store the regression equation in our Why menu. So we go from here to variables VRs over to why variables choose function and choose why one. Now we can calculate the regression model. Why equals approximately 1.88 x plus about 82.6. And if we go into the y equals men, you will see that that has been pasted in. So now we compress graph, and there's our regression line going right through the data. Finally, if we're given a human femur length of 53 centimeters, we want to approximate the height based on this model. So what we can do is use a table for that a table or a graph. But I prefer the table, so I'm going to go into the table set menu, which is second window. Make sure that my independent setting is on ask. That allows me to type in my own X values and then go into the table, which is second Graf type in the X value of 53 and we get a Y value of 182.33 So that's telling us that a person with a femur length of 53 centimeters would probably have a height of about 182 centimeters.
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