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# Using the correlation coefficient

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Calculate, test, and interpret the relationship between two variables using the correlation coefficient.

The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.

City Police Number of Crimes City Police Number of Crimes
Oxford 23 18 Holgate 24 9
Starksville 24 15 Carey 20 22
Danville 30 9 Whistler 19 24
Athens 33 11 Woodville 27 10

(a) Determine the regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign).

formula304.mml = + X

(b) Estimate the number of crimes for a city with 21 police officers. (Round your answer to 4 decimal places).

Number of crimes

(c) Interpret the regression equation.

For each policeman added, the number of crimes goes by one.

https://brainmass.com/statistics/correlation/relationship-variables-correlation-coefficient-517585

## SOLUTION This solution is FREE courtesy of BrainMass!

(a). mean of police (x)=(23+24+30+33+24+20+19+27)/8=25
Sxx=(23-25)^2+...+(27-25)^2=160
mean of crimes (y)=(18+15+...+10)/8=14.75
Sxy=(23-25)*(18-14.75)+...+(27-25)*(10-14.75)=-161
slope=Sxy/Sxx=-161/160=-1.0063
intercept=mean of y-slope*mean of x=14.75+1.0063*25=39.9075

Therefore, the regression equation is y=-1.0063x+39.9075

(b)when x=21, y=-1.0063*21+39.9075=18.7752
(c) For each policeman added, the number of crimes reduces by 1.0063.

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