A sociologist believes that the crime rate in an area is significantly influence

Question

A sociologist believes that the crime rate in an area is significantly influenced by the area’s poverty rate and median income. Specifically, she hypothesizes crime will increase with poverty and decrease with income. She collects data on the crime rate (crimes per 100,000 residents), the poverty rate (in %), and the median income (in $1,000s) from 41 New England cities. A portion of the regression results is shown below.

Standard Coefficients Error t Stat p-value

Intercept 301.62 549.71 0.55 0.5864

Poverty 53.16 14.22 3.74 0.0006

Income 4.95 8.26 0.60 0.5526

(a) Are the signs as expected on the slope coefficients? (b) Interpret the slope coefficient for Poverty. (c) Predict the crime rate in an area with a poverty rate of 20% and a median income of $50,000.

Explanation / Answer

a.

No, coefficient of income is showing positive sign. But, it should show negative sign because crime will decrease with increase in income and vice versa as per the sociologist. Thus, there seems to be negative relationship. Although, positive sign of coefficient of income does not reflect the same.

b.

Slope coefficient of poverty is 53.16. It means that 1 unit (Percentage) increase in poverty will cause an increase of 53.6 unit in crime and vice versa with other independent variables remain constant. Here unit is the number or rate.

c.

as per the data in question,

Crime rate = -301.62 +   53.16*(Poverty) + 4.95*(income)

Crime rate = -301.62 + 53.16*20 + 4.95*50 = 1009.08 or 1009

Thus, crime rate is 1009 per 100,000 residents.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.