Question

A recent analysis of data for the 50 U.S. States on crime found the regression equation y=209.9+27.2xy=209.9+27.2x, where xx is the poverty rate and yy is the violent crime rate (measured as number of violent crimes per 100,000 people in the state).

1. Interpret the slope of this line.
2. Interpret the y-intercept of this line. Does this make sense in context of the problem?
3. The state poverty rates ranged from 8.3 (Hawaii) to 27.2 (Mississippi). Over this range, find the range of predicted values of violent crime rate. Explain your process.
4. Would the correlation between these variables be positive or negative? Why?

Answer 1

(a) The slope is 27.2, it can be interpreted as the amount of change in the dependent variable "violent crimes rate" with 1 unit change in the independent variable "poverty rate". If we increase the "poverty rate" by 1 unit, the "violent crimes rate" increases by 27.2 units.

(b) The y-intercept is 209.9, it can be interpreted as the expected value of the violent crimes rate when the poverty rate is zero. It doesn't make any practical sense because the poverty rate of any places equal to zero is very unusual.

(c) Predicted value of violent crimes rate in Hawaii = 209.9 + 27.2*8.3 = 435.66 (Minimum)

Predicted value of violent crimes rate in Mississippi = 209.9 + 27.2*27.2 = 949.74 (Maximum)

The range of predicted values of violent crime rate is 435.66 to 949.74. Hence, the expected number of violent crimes per 100,000 people in the United States is between 435.66 and 949.74.

(d) As the poverty rate increases, the violent crimes rate also increases. Hence, both variables are on the same direction and thus the correlation between these variables are positive.