4. Section 14.3, A sociologist believe that the crime rate in an area is signifi

Question

4. Section 14.3, A sociologist believe 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 crime rate (crimes per 100,000 residents), the poverty rate (%), and the median income (in $1,000) from 41 New England cities. A portion of the regression result is shown below. Table 1: Coefficients Standard 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 0.6 0.5526 (a) Are the signs as expected on the slope coefficients? (b) Interpret the slope coefficient for poverty. (c) What is the sample regression equation? Predict the crime rate in an area with poverty rate of 20% and a median income of $50,000.

Explanation / Answer

Here the regression equation is

crime rate=-301.62+53.16 Poverty+4.95 Income

a) As Income increases, income should decrease according to her hypothesis, but the coefficient of income in the regression equation is 4.95 >0. But we are expecting a negative sign here.

b) For a unit increase in area's poverty rate, the crime rate in an area will increase by 53.16 unit.

c) the predicted crime rate in an area with poverty rate of 20% and a median income of $50,000

=-301.62+(53.16*20)+(4.95*50)=1009.08

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

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