Question

Homicide and suicide are both intentional means of ending a life. However, the reason for committing a homicide is different from that for suicide and we might expect homicide and suicide rates to be uncorrelated. On the other hand, both can involve some degree of violence, so perhaps we might expect some level of correlation in the rates. The data from 2008-2011 for 26 counties in Ohio are shown in the table. Rates are per 100,000 people County Homicide rate Suicide rate County Homicide rate Suicide rate 9.9 15.5 12.8 16.0 13.6 15.2 Montgomery 9.8 8.2 11.3 11.3 10.7 12.9 13.2 Allen Ashtabula Butler Clermont Clark Columiana Cuyhoga Delaware Franklin Greene Hamilton Lake Licking Lorain Lucas Mahoning Medina Miami 15.6 12.8 11.4 10.0 9.6 15.5 11.9 13.0 11.5 16.1 9.6 10.8 8.4 2.8 2.7 7.6 10.6 5.4 9.5 10.0 Portage Stark Summit Trumbull Warren Wayne Wood 4.8 8.8 2.7 9.2 6.8 1.0 1.0 4.0 (a) Make a scatterplot that shows how suicide rate can be predicted from homicide rate. There is a weak linear relationship. with correlation r0.17 Each of the scatterplots in the choices has a relationship fitted to the plot. Select the plot that corresponds with the correlation of 0.17 Suicide vs. Homicide 18 16 14 C0 12 10 8 2.5 5.0 10.0 0.0 7.5 Homicide Suicide vs. Homicide 18 16. 14 12 10 8 10.0 7.5 5.0 2.5 0.0 Homicide Suicide vs. Homicide 18 16. 14 12 14 12 10 8 7.5 10.0 2.5 5.0 0.0 Homicide Suicide vs. Homicide 18 16. 14 CO 12 10 8 10.0 7.5 2.5 5.0 0.0 Homicide (b) Find the least-squares regression line for predicting suicide rate from homicide rate, a + b × homicide answers rounded to three decimal places.) Enter your (c) Explain in words what the slope of the regression line tells us. O The slope means that for every additional suicide (per 100,000 people), there is an average increase of 0.126 O The slope means that for every additional homicide (per 100,000 people), there is an average decrease of 0.126 O The slope means that for every additional homicide (per 100,000 people), there is an average increase of 0.126 O The slope means that for every additional homicide (per 100,000 people), there is an average increase of 11.640 O The slope means that for every additional homicide (per 100,000 people), there is an average decrease of 11.640 homicide (per 100,000 people) in these Ohio counties. suicide (per 100,000 people) in these Ohio counties. suicide (per 100,000 people) in these Ohio counties. suicides (per 100,000 people) in these Ohio counties. suicides (per 100,000 people) in these Ohio counties. (d) Another Ohio county has a homicide rate of 8.0 per 100,000 people. What is the county's predicted suicide rate? (Enter your answer rounded to three decimal places.) Predicted suicide rate: per 100,000 people

Answer 1

SOLUTION

Answer a) A scatterplot of homicide rate and suicide rate is, By using Excel software, draw scatterplot with the help of following steps 1)Import the data 2) Select the MegaStat from Add-Ins option. 3) Selectthe Scatterplot from Regression. 4)Select data input. 5) Select Plot linear regression line. 6) Click Ok.

Scatterplot of homiside rate and suicide rate 17 16 15 o 14 13 12 y 0.126 x11.640 R2 0.029 10 10 12 4. Homiside rate From the Excel output, a scatterplot of Percent scatterplot of homicide rate and suicide rate conclude there is a weak positive relationship between homicide rate and suicide rate

b) The least-squares regression line for predicting suicide rate (y) on homicide rate (x) is, By using Excel software, find regressionequation with help offollowing steps 1) Import the data. 2) Select Data Analysis from Data menu. 3) SelectRegression and click Ok. 4)Input Y Range and Input X range 5) Click Ok. SUMMARY OUTPUT Coefficients Standard Error tStat P-value Intercept Homiside rate 11.6396388 0.793333923 14.6718 1.76E-13 0.12585038 0.149202258 0.843488 0.407284 From the Excel output, the least-squares regression line for predicting suicide rate (v) on homicide rate (r) is,

-11.640 +0.126 x Interpretation of slop β1-0.126. For each unit increase in homicide rate, the mean suicide rate is estimated to increases 0.126. d) The country's predict suicide rate when homicide rate 8.0 is, 11.640 0.126 x 8.0 12.648 The country's predict suicide rate when homicide rate 8.0 is 126.48