Preventing suicide is a important issue facing mental health workers. Predicting geographic regions where the risk of suicide is high could help people decide where to increase or improve mental health resources and care. Some psychiatrists have argued that homicide and suicide may have some causes in common. If so, one would expect homicide and suicide rates to be correlated. And if this is true, areas with high rates of homicide might be predicted to have high rates of suicide and therefore be in need of increased mental health resources. Research has had mixed results, including some evidence that there is a positive correlation in certain European countries but not in the United States. Here are data from 2015 for the 1111 counties in Ohio with sufficient data for homicides and suicides to allow for estimating rates for both. Rates are per 100,000 people.100,000 people. County Homicide Rate Suicide Rate Butler 4.04.0 11.211.2 Clark 10.810.8 15.315.3 Cuyahoga 12.212.2 11.411.4 Franklin 8.78.7 12.312.3 Hamilton 10.210.2 11.011.0 Lorain 3.33.3 14.314.3 Lucas 6.06.0 12.612.6 Mahoning 11.711.7 15.215.2 Montgomery 8.98.9 15.715.7 Stark 5.85.8 16.116.1 Summit 7.17.1 17.917.9 To access the data, click the link for your preferred software format. CSV Excel (xls) Excel (xlsx) JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS TI CrunchIt! © Macmillan Learning Make a scatterplot that shows how suicide rate can be predicted from homicide rate. There is a weak linear relationship, with correlation ?=−0.0645.�=−0.0645. Find the least-squares regression line for predicting suicide rate from homicide rate, suicide rate=?+?×(homicide rate).suicide rate=�+�×(homicide rate). Add this line to your scatterplot. Give your answers to three decimal places. ?=�=

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Preventing suicide is a important issue facing mental health workers. Predicting geographic regions where the risk of suicide is high could help people decide where to increase or improve mental health resources and care. Some psychiatrists have argued that homicide and suicide may have some causes in common. If so, one would expect homicide and suicide rates to be correlated. And if this is true, areas with high rates of homicide might be predicted to have high rates of suicide and therefore be in need of increased mental health resources. Research has had mixed results, including some evidence that there is a positive correlation in certain European countries but not in the United States. Here are data from 2015 for the 1111 counties in Ohio with sufficient data for homicides and suicides to allow for estimating rates for both. Rates are per 100,000 people.100,000 people.

County	Homicide Rate	Suicide Rate
Butler	4.04.0	11.211.2
Clark	10.810.8	15.315.3
Cuyahoga	12.212.2	11.411.4
Franklin	8.78.7	12.312.3
Hamilton	10.210.2	11.011.0
Lorain	3.33.3	14.314.3
Lucas	6.06.0	12.612.6
Mahoning	11.711.7	15.215.2
Montgomery	8.98.9	15.715.7
Stark	5.85.8	16.116.1
Summit	7.17.1	17.917.9

To access the data, click the link for your preferred software format.

CSV Excel (xls) Excel (xlsx) JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS TI CrunchIt!

Make a scatterplot that shows how suicide rate can be predicted from homicide rate. There is a weak linear relationship, with correlation ?=−0.0645.�=−0.0645. Find the least-squares regression line for predicting suicide rate from homicide rate, suicide rate=?+?×(homicide rate).suicide rate=�+�×(homicide rate). Add this line to your scatterplot. Give your answers to three decimal places.

?=�=

Expert Solution

Step 1

The given data is as follows.

Homicide Rate	Suicide rate
4.0	11.2
10.8	15.3
12.2	11.4
8.7	12.3
10.2	11.0
3.3	14.3
6.0	12.6
11.7	15.2
8.9	15.7
5.8	16.1
7.1	17.9

The independent variable $X$ is the Homicide rate

The dependent variable $Y$ is the Suicide rate

The formula for the correlation coefficient is as follows.

$r = \frac{n \sum_{}^{} x y - \sum_{}^{} x \sum_{}^{} y}{\sqrt{[{n \sum}_{i = 1}^{n} x^{2} - {(\sum_{}^{} x)}^{2}] [{n \sum}_{i = 1}^{n} y^{2} - {(\sum_{}^{} y)}^{2}]}}$

$x$ and $y$ are the sample means

$x = \frac{\sum_{i = 1}^{n} x_{i}}{n} y = \frac{\sum_{i = 1}^{n} y_{i}}{n}$

$n$ is the sample size.

The simple linear regression line is as follows.

$y = a + b x$

$x$ is the independent variable.

$y$ is the dependent variable.

$a = \frac{\sum_{} y \sum_{} x^{2} - \sum_{} x \sum_{} x y}{\underset{}{n \sum} x^{2} - {(\sum_{} x)}^{2}} b = \frac{n \sum_{} x y - \sum_{} x \sum_{} y}{\underset{}{n \sum} x^{2} - {(\sum_{} x)}^{2}}$