The city council of Pine Bluffs is considering increasing the number of police i

Question

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 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. (a) Determine the regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.) (b) Estimate the number of crimes for a city with 23 police officers. (Round your answers to 4 decimal places.) (c) Interpret the regression equation.

Explanation / Answer

Sol:

Run regression in excel.

y=no of crimes

x=police

we can see correlation coeff=0.89

strong positive relationship exists between two

regression eq is

number of crimes=31.8383-0.9453(police)

slope=-0.9453

yintercept=31.8383

Solutionb:

police officers=23

no of crimes=31.8383-0.9453(police)

=31.8383-0.9453(23)

=10.09

no of crimes=10

(round to nearest integer)

Solutionc:

slope is -0.945 approximately one

slope=m=change in y/change in x

-1(change in police)=change in no of crimes

Goes down by 1

SUMMARY OUTPUT Regression Statistics Multiple R 0.893871 R Square 0.799006 Adjusted R Square 0.765507 Standard Error 2.867751 Observations 8 ANOVA df SS MS F Significance F Regression 1 196.156 196.156 23.85168 0.002756 Residual 6 49.34396 8.223994 Total 7 245.5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 31.83827 4.236351 7.515494 0.000287 21.47229 42.20425 police -0.94533 0.193564 -4.88382 0.002756 -1.41896 -0.4717

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