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A study of emergency service facilities investigated the relationship between the numberof facilities and the average distance traveled to provide the emergency service. The fol-lowing table gives the data collected.$\begin{array}{l}{\text { a. Develop a scatter diagram for these data, treating average distance traveled as the }} \\ {\text { dependent variable. }} \\ {\text { b. Does a simple linear model appear to be appropriate? Explain. }} \\ {\text { c. Develop an estimated multiple regression equation for the data of the form }} \\ {y=b_{0}+b_{1} x+b_{1} x^{2}}.\end{array}$

a) see tableb) The scatter diagram follows a curvilinear path therefore, suggesting an estimated regressionequation of the form $\hat{y}=b_{0}+b_{1} x+b_{2} x^{2}$ . Simple linear model does not appear to be suitable.c) $\hat{y}=2.9016-0.1848 x+0.0035 x^{2}$

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Temple University

University of North Carolina at Chapel Hill

Piedmont College

Lectures

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02:04

The graph shown models the…

01:31

The number of engines own…

02:30

The table below lists the …

01:29

The numbers of freestan…

01:25

The following table provid…

01:54

The scatterplot above show…

A regression was run to de…

00:59

The accompanying graph plo…

05:41

[T] The following table pr…

07:48

Refer to the data presente…

06:23

The following table shows …

03:25

Data from the U.S. Departm…

01:12

Vehicle Waiting Time The a…

01:18

01:14

Draw a scatter diagram for…

02:47

The "In the eye of th…

04:51

A mathematical model can b…

02:50

The accompanying graph sho…

For each of the following …

So in this question, were given some data about the number of facilities and the average distance. And we're basically as toe get. Have a scatter plot off average distance as a functional number off facilities. So average distance is basically the Y axis. So let's go ahead and insert a scatter plot right here. Sonar By access, we have average distance. And in our X axis we have the number of facilities and we can see that the number off the average distance decreases as the number of facilities increases. So this is our answer to part A. We have our schedule cloud over here. Well, in part B were asked if a simple linear model appears to be adequate so we can actually see here that this shows a more curvy linear relationship. So a linear model does not appear to be adequate. So let's write that down. Linear model does not appear to be adequate because we can see that there is a data herds over time and is not linear for ST right. So that's our answer to parties that the linear model does not appear to be adequate now. In party were asked to develop a regression equation off the form that has zero plus B one x plus B two x squared. So let's go ahead and do that. So average distance with our why, variable, We're gonna put that over here. Number of facilities we're gonna call it X, and then we're gonna have another variable X squared, which is basically equals two. Everything in the first column squared. So we basically have thes two X variables, and we have our y variable and let's go ahead and develop a multiple regression equation. So to do that, we're going to put our input wide range, which is C one through C seven. Yeah, Then we have our input X range, which goes from a one through B seven. He said, Our confidence level to be 95% and we're gonna put the output right about here. So we're gonna put the output that let's go back and make sure X ranges correct. So X range. Okay, then our output range is going to be, Yeah, right here is 67. You don't need any plots, so let's go ahead and get that. So, with the output we see r r squared is pretty high. The relationship is significant for why end two variables as well as for some of the individual variables. So let's just go ahead and write that equation down. So we have. For part C or answer. Ruby Wise equals two 2.9 you tu minus 0.18 486 plus 4860.0 We fly born x square. So this is our answer to park sweep. Thank you. Stuff right here we have our scatter plot. In part, a answer to Part B explaining the linear model is not adequate and answered Part C, which has the X and the X squared trump in our multiple regression equation.

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