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 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 15 17   Holgate 17 7   Starksville 17 13   Carey 12 21   Danville 25 5   Whistler 11 19   Athens 27 7   Woodville 22 6 (a) Determine the standard error of estimate. (Round your answer to 4 decimal places.)

   (b) Determine the coefficient of determination. (Round your answer to 4 decimal places.)

(c) Interpret the coefficient of determination.

_________percent of the variation in the number of crimes can be explained by the variation in the number of police.

Explanation / Answer

The statistical software output for the given problem is:

Simple linear regression results:
Dependent Variable: Number of Crimes
Independent Variable: Police
Number of Crimes = 29.388199 - 0.95962733 Police
Sample size: 8
R (correlation coefficient) = -0.87439563
R-sq = 0.76456771
Estimate of error standard deviation: 3.3783962

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) Standard error = 3.3784

b) Coefficient of determination = 0.7646

c) 76.46 percent of the variation in the number of crimes can be explained by the variation in the number of police.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 29.388199 4.1433806 0 6 7.092807 0.0004 Slope -0.95962733 0.21739623 0 6 -4.4141856 0.0045

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