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When laboratory rats are exposed to asbestos fibers, some of them develop lung tumors. The table lists the results of several experiments by different scientists.

(a) Find the regression line for the data.(b) Make a scatter plot and graph the regression line. Does the regression line appear to be a suitable model for the data?(c) What does the y-intercept of the regression line represent?

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02:10

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

Johns Hopkins University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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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.

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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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all right. This problem is another great one for a graphing calculator, and we want to start by going into the stat menu and going into edit and then typing all of our data into list one and list, too. List. One is Thea's best dose exposure analyst to is the percent of mice that developed lung tumors. Good, uplifting problem that we're looking at here and we want to find the regression line. So once we have the numbers typed in, we can go back to stat Over to calculate and down to choice number four. Linear regression Press enter. We're going to use list one. Endless to We don't need to worry about frequency list, and we are going to be interested in plot in part B to look at the plot and look at the graph. So let's go ahead and store this in. Ah, why the wine menu? So we go to variables. We go over to why variables and choose function and choose why one. And now we can calculate. So the regression equation is approximately. Why equals 0.19 x plus, 0.305 And if we press why equals we noticed that that equation was pasted in to the y equals menu in a great deal of detail. You see all these numbers so we're not gonna lose accuracy on rounding there when we look at that graph. So the next thing we want to do for part B is to make the scatter plot and graft the regression line. So the regression line equation has already turned on, and now we need to turn on the scatter plot. So go into the second y equals menu to take me to stab plots to go into the menu first at plot number one and turn it on and noticed that we want to choose Scatter plot list one and list, too. Okay, So now to choose a good window for this data, we're going to go to Zoom and chew Zoom nine, which is zoom stat. So here we see our scatter plot and we see the regression line. I would say it does appear to be a suitable model, because that line does go through the data fairly nicely. With a few points above and a few points below on the line, the data does appear to be somewhat linear. It doesn't fall super close to the line, but it's having sort of a linear trend. Okay, finally, for part C, we want to say what the Y intercept of the regression line represents, so the Y intercept is the point with an ex coordinative zero. And that would mean that there mice had or the rats had zero exposure to ESP. Estos and that would be the rate of, or the percent of mice that develop lung tumors, even though they had no ESP estos exposure, and we could go ahead and find what that is. So if we go into table set, which is second window, and we make sure that we're on independent ask and then we go into table, which is second graf, we can type in a zero for the X coordinate, and we get our Y coordinate of 0.3 0.30 for eight. So that would represent about a 0.3% of mice developing lung tumors, even though they weren't exposed to asbestos

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