14 points QUESTION 3 The number of crimes reported (in millions) and the number

Question

14 points QUESTION 3 The number of crimes reported (in millions) and the number of arrests reported (in millions) by the U.S. Department of Justice for 14 years Adapted from the National Crime Victimization Survey and Uniform Crime Reports) Crimes,1.60 155 1.44 1.40 1.32 1.23 1.22 Arrests, 7s 0.30 6.73 72 068 064 a 63 Crimes,x 123 12z 118 1.16 1.19 121 120 Arrests y 63 062 0 as9 as 061 os8 a) Find the regression equation that models the number of crimes as a function of the number of arrests is y = b) The correlation coefficient is R c) The linear correlation coefficient is R = d) SST = x + e) SSR = f) SSE = ROUND ALL ANSWERS TO 4 DECIMAL PLACES X.XXXx

Explanation / Answer

Question 3

Solution:

Regression model for the prediction of dependent variable number of arrests is summarised as below:

(Regression output by using Excel)

Regression Statistics

Multiple R

0.9806

R Square

0.9615

Adjusted R Square

0.9583

Standard Error

0.0147

Observations

14

ANOVA

df

SS

MS

F

P-value

Regression

1

0.0650

0.0650

299.6730

0.0000

Residual

12

0.0026

0.0002

Total

13

0.0676

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

0.0206

0.0370

0.5555

0.5887

-0.0601

0.1012

X

0.4916

0.0284

17.3111

0.0000

0.4297

0.5534

Part a

Required regression equation for the prediction of number of arrests is given as below:

Y = 0.4916*X + 0.0206

Part b

The coefficient of determination or the value of R-square is given as below:

R2 = 0.9615

About 96.15% of the variation in the dependent variable number of crimes is explained by the independent variable number of crimes.

Part c

The linear correlation coefficient is given as R = 0.9806

There is a very strong positive linear relationship exists between given two variables number of crimes and number of arrests.

Part d

SST = 0.0676

Part e

SSR = 0.0650

Part f

SSE = 0.0026

(All values are taken from above ANOVA table for regression model.)

Regression Statistics

Multiple R

0.9806

R Square

0.9615

Adjusted R Square

0.9583

Standard Error

0.0147

Observations

14

ANOVA

df

SS

MS

F

P-value

Regression

1

0.0650

0.0650

299.6730

0.0000

Residual

12

0.0026

0.0002

Total

13

0.0676

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

0.0206

0.0370

0.5555

0.5887

-0.0601

0.1012

X

0.4916

0.0284

17.3111

0.0000

0.4297

0.5534

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