Question

The following data represent property crime rate against individuals (crimes per 1000 households) and their household income (in dollars) in the United States in 2009 . $$ \begin{array}{|cc|} \hline \begin{array}{l} \text { Income } \\ \text { Level } \end{array} & \begin{array}{c} \text { Property } \\ \text { Crime Rate } \end{array} \\ \hline 5000 & 201.1 \\ 11,250 & 157.0 \\ 20,000 & 141.6 \\ 30,000 & 134.1 \\ 42,500 & 139.7 \\ 62,500 & 120.0 \\ \hline \end{array} $$ (a) Using a graphing utility, draw a scatter diagram of the data using income, $x$, as the independent variable and crime rate, $y,$ as the dependent variable. (b) Based on the scatter diagram drawn in part (a), decide on a model (linear, quadratic, cubic, exponential, logarithmic, or logistic) that you think best describes the relation between income and crime rate. Be sure to justify your choice of model. (c) Using a graphing utility, find the model of best fit. (d) Using a graphing utility, draw the model of best fit on the scatter diagram you drew in part (a). (e) Use your model to predict the crime rate of a household whose income is $\$ 55,000$.

          The following data represent property crime rate against individuals (crimes per 1000 households) and their household income (in dollars) in the United States in 2009 .
$$
\begin{array}{|cc|}
\hline \begin{array}{l}
\text { Income } \\
\text { Level }
\end{array} & \begin{array}{c}
\text { Property } \\
\text { Crime Rate }
\end{array} \\
\hline 5000 & 201.1 \\
11,250 & 157.0 \\
20,000 & 141.6 \\
30,000 & 134.1 \\
42,500 & 139.7 \\
62,500 & 120.0 \\
\hline
\end{array}
$$
(a) Using a graphing utility, draw a scatter diagram of the data using income, $x$, as the independent variable and crime rate, $y,$ as the dependent variable.
(b) Based on the scatter diagram drawn in part (a), decide on a model (linear, quadratic, cubic, exponential, logarithmic, or logistic) that you think best describes the relation between income and crime rate. Be sure to justify your choice of model.
(c) Using a graphing utility, find the model of best fit.
(d) Using a graphing utility, draw the model of best fit on the scatter diagram you drew in part (a).
(e) Use your model to predict the crime rate of a household whose income is $\$ 55,000$.

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Added by Brooke C.

Grade 6 Mathematics: Open Up Resources, Common Core State Standards Edition

N/A 6th Edition

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Solved by Expert Jerelyn Nevil

01/07/2023

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The following data represent property crime rate against individuals (crimes per 1000 households) and their household income (in dollars) in the United States in 2009 . $$ \begin{array}{|cc|} \hline \begin{array}{l} \text { Income } \\ \text { Level } \end{array} & \begin{array}{c} \text { Property } \\ \text { Crime Rate } \end{array} \\ \hline 5000 & 201.1 \\ 11,250 & 157.0 \\ 20,000 & 141.6 \\ 30,000 & 134.1 \\ 42,500 & 139.7 \\ 62,500 & 120.0 \\ \hline \end{array} $$ (a) Using a graphing utility, draw a scatter diagram of the data using income, $x$, as the independent variable and crime rate, $y,$ as the dependent variable. (b) Based on the scatter diagram drawn in part (a), decide on a model (linear, quadratic, cubic, exponential, logarithmic, or logistic) that you think best describes the relation between income and crime rate. Be sure to justify your choice of model. (c) Using a graphing utility, find the model of best fit. (d) Using a graphing utility, draw the model of best fit on the scatter diagram you drew in part (a). (e) Use your model to predict the crime rate of a household whose income is $\$ 55,000$.

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Transcript

00:01 That you need help with this problem and it says the following data represents property crime rate against individual crimes 1 ,000 per household in their household income in dollars in the united states in 2009.

00:12 So using a graphing utility, dry scatter diagram of this data using income x as the independent variable and crime rate y is a dependent variable.

00:22 So i'm going to show you how to use excel in order to solve this problem.

00:27 So first thing i'm going to do is i'm going to highlight the information, the income level is going to be x, and property crime rate is going to be y, the dependent variable.

00:37 And i'm going to insert a scatter diagram, and it says here, based on the scatter diagram, draw in part, and decide a model, linear, quadratic, cubic, exponential, or logarithmic, or logistic.

00:56 So if i go to add chart and i want to add a trend line there's all of these different options that i do have and i'm going to say that this is linear yes there is a little bit of a curvature here so i could delete this and we can see what a trend line that's exponential looks like but again it will be pretty linear again so i'm going to delete this and i'm going to move back to a linear trend line.

01:33 And so then what i'm going to do is i'm going to display the equation in the chart.

01:41 And i'm going to make it bold and bigger.

01:48 And this is the equation that i'm going to get.

01:53 And it says using the graphing utility, find the model best fit.

01:58 So i did do that...

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