8.25 Murders and poverty, Part I

Title

A. Write out the linear model

Annual Murders per Million = -29.901 + 2.559*poverty%

B. Interpret the intercept

Intercept represents the Baseline in a model and here it is negative and significant. This could mean the following: A. The model may be predicting outside the observed range of values for the Y and X variables. When poverty% is Zero, the model is stating that Annual Murders (per million) will be negative. In real world it can only go as low as zero Murders and not predict a negative number of murders. In the chart it is seen that poverty% varies from a low of approximately 14% to a high of about 26%. What that means is that we cannot interpret the model intercept outside the observed range of values for poverty% [when poverty% = 0 it is very much outside the range of 14%-26%]

C. Interpret the Slope

The slope for poverty% is positive and significant. The value of 2.559 means that as poverty% increases by 1% point, Annual Murders per million increase by approximately 2.6 - In a linear extrapolation we could conclude that a 10% increase in poverty% will result in an increase of 26 Annual Murders per million.

D. Interpret R2

The model R-square is 70.52% - this means that poverty% variable as a predictor is able to explain approximately 71% variation in the Annual Murders per million Dependent variable. That represents a strong and significant ability of the predictor to account for the variation in the dependent variable.

E. Calculate the correlation coefficient

In a regression model with just one predictor, the R-square represents the square of the correlation coefficient. Hence the correlation coefficient is obtained by taking the square-root of the R-square (70.52%). Hence the Correlation Coefficient is 0.8397