State level data were used to regress “violent crime rate (violent crimes per 10

Question

State level data were used to regress “violent crime rate (violent crimes per 100,000 population)” on several independent variables. Answer the following questions based on the reported SPSS output.

a.   Identify the regression line produced by this analysis.

b.   How much variation in the dependent variable is accounted for by the independent variables?

c.   Interpret the regression coefficients for “household median income.”

d.   Which of the regression coefficients are statistically significant at the 95% confidence level?

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.711a

.506

.463

197.45009

a. Predictors: (Constant), HOUSEHOLD MEDIAN INCOME (in $1,000 per capita), Population (in 1,000s) per square mile, MARRIAGES PER 1,000 POP, 1984 , PERCENT W 12+ YEARS EDUCATION 1980

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

348.791

256.901

1.358

.181

MARRIAGES PER 1,000 POP, 1984

2.395

1.843

.136

1.300

.200

PERCENT W 12+ YEARS EDUCATION 1980

-8.372

4.843

-.233

-1.729

.091

Population (in 1,000s) per square mile

126.538

20.180

.652

6.270

.000

HOUSEHOLD MEDIAN INCOME (in $1,000 per capita)

34.651

14.915

.311

2.323

.025

a. Dependent Variable: Violent crimes per 100,000 populations

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.711a

.506

.463

197.45009

a. Predictors: (Constant), HOUSEHOLD MEDIAN INCOME (in $1,000 per capita), Population (in 1,000s) per square mile, MARRIAGES PER 1,000 POP, 1984 , PERCENT W 12+ YEARS EDUCATION 1980

Explanation / Answer

a) Equation:

Violent rate = 348.791 + 2.395 * MARRIAGES PER 1,000 POP - 8.372 * PERCENT W 12+ YEARS EDUCATION + 126.538 * Population (in 1,000s) per square mile + 34.651 * HOUSEHOLD MEDIAN INCOME (in $1,000 per capita)

b) R^2 = 0.506

So, 50.6% of the variation in the dependent variable is accounted for by the independent variables.

c) Coefficient of HOUSEHOLD MEDIAN INCOME = 34.651

It tells that if HOUSEHOLD MEDIAN INCOME rises by $1000 per capita, violent rate will increase by 34651

d) If the p-value is less than or equal to the alpha (p< .05), then we reject the null hypothesis, and we say the result is statistically significant.

So, Constant, MARRIAGES PER 1,000 POP, 1984 and PERCENT W 12+ YEARS EDUCATION 1980 are statistically significant.

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