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 16 14 Holgate 19 6 Starksville 19 13 Carey 14 17 Danville 24 6 Whistler 13 20 Athens 27 7 Woodville 21 8 PictureClick here for the Excel Data File a. Determine the regression equation. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.) formula14.mml = + X b. Estimate the number of crimes for a city with 28 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 (Click to select)downup by one.

Explanation / Answer

The excel output is given by:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.858139951

R Square

0.736404176

Adjusted R Square

0.692471539

Standard Error

2.992785732

Observations

8

ANOVA

df

SS

MS

F

Significance F

Regression

1

150.1344014

150.1344

16.76212

0.006399271

Residual

6

53.74059862

8.956766

Total

7

203.875

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

29.73676132

4.607998945

6.453292

0.000656

18.46139411

41.01212853

18.46139411

41.01212853

Police

-0.960092095

0.234503004

-4.09416

0.006399

-1.533900274

-0.38628392

-1.533900274

-0.386283917

RESIDUAL OUTPUT

Observation

Predicted Number of Crimes

Residuals

1

14.3752878

-0.375287797

2

11.49501151

-5.495011512

3

11.49501151

1.504988488

4

16.29547199

0.704528012

5

6.694551036

-0.694551036

6

17.25556408

2.744435917

7

3.814274751

3.185725249

8

9.574827322

-1.574827322

a. The regression equation is : y=29.7368-0.9601*x

where,y=Number of crimes

x=Police

b. The estimated no. of crimes for a city with 28 police officers is: 2.854 i.e. approximately 3.

c.Interpretation of regression equation

If y is increased by 1 then x is decreased by 0.9601.(Literally)

i.e. If number of police is increased by 1 then number of crime in particular city is decreased by 1 approximately.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.858139951

R Square

0.736404176

Adjusted R Square

0.692471539

Standard Error

2.992785732

Observations

8

ANOVA

df

SS

MS

F

Significance F

Regression

1

150.1344014

150.1344

16.76212

0.006399271

Residual

6

53.74059862

8.956766

Total

7

203.875

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

29.73676132

4.607998945

6.453292

0.000656

18.46139411

41.01212853

18.46139411

41.01212853

Police

-0.960092095

0.234503004

-4.09416

0.006399

-1.533900274

-0.38628392

-1.533900274

-0.386283917

RESIDUAL OUTPUT

Observation

Predicted Number of Crimes

Residuals

1

14.3752878

-0.375287797

2

11.49501151

-5.495011512

3

11.49501151

1.504988488

4

16.29547199

0.704528012

5

6.694551036

-0.694551036

6

17.25556408

2.744435917

7

3.814274751

3.185725249

8

9.574827322

-1.574827322

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