Question

(a) 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 2626 counties in Ohio. Rates are per 100,000100,000 people is given in the table.

HomicideSuicide Rate HomicideSuicide County Countv Rate Rate Rate Allen 3.8 9.9 Lorain 3.6 15.6 Ashtabula 2.8 15.5 Lucas 7.6 12.8 Butler 2.7 12.8 Mahoning 10.6 11.4 Clermont 16.0 Medina 10.0 Clark 5.4 13.6 Miami 1.0 9.6 Columbiana 3.4 15.2Montgomery 9.5 15.5 Cuyahoga 9.8 8.2 11.3 11.3 10.0 Portage 11.9 Delaware Stark 4.8 13.0 Franklirn 8.8 Summit 4.9 11.5 16.1 9.6 10.8 Greene 2.7 Trumbull 6.8 Hamiltorn 9.2 10.7 Warren Lake 12.9 Wayne Licking 4.0 13.2 Wood 1.0 8.4

(a) Using the software of your choice make a scatterplot of the data. What is the correlation between homicide rate and suicide rate from 2008‑2011 for the 2626 counties in Ohio in the table shown? (Enter your answer rounded to three decimal places.)

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(b) Using the software of your choice make a scatterplot of the data with one new point added. Point A: homicide rate 3030 , suicide rate 3030 . Find the new correlation for the original data plus Point A. (Enter your answer rounded to three decimal places.)

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(c) Using the software of your choice, make a scatterplot of the data with a different new point added. Point B: homicide rate 1010 , suicide rate 5.55.5 . Find the new correlation for the original data plus Point B. (Enter your answer rounded to three decimal places.)

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(d) By looking at your plot, explain why adding Point A makes the correlation stronger (closer to 11 ) and adding Point B makes the correlation weaker (closer to 00 ).

Point A strengthens the ( negative or positive )

linear association because, when ( A or B)

is included, the points of the scatterplot seem to actually have a ( linear or nonlinear)

relationship (your eye is drawn to that point in the upper right). Meanwhile, Point B (at the lower right of the graph) (blind with or deviates from)

the pattern, weakning or strenthing

the association.

Answer 1

a) Scatter plot:

Using Excel Function CORREL(array1,array2):

Correlation, r = 0.170

b) Scatter plot after adding point A(30,30)

Using Excel Function CORREL(array1,array2):

Correlation, r = 0.746

c) Scatter plot after adding point b(10, 5.5)

Using Excel Function CORREL(array1,array2):

Correlation, r = -0.017

d) Point A strengthens the positive linear association because, when A is included, the points of the scatter plot seem to actually have a linear relationship (your eye is drawn to that point in the upper right). Meanwhile, Point B (at the lower right of the graph) deviates from the pattern, weakning the association.