Exercise presentation OpenIntro Stats 7.29

DATA 606 MSDA CUNY

7.29 Murders and poverty, Part I. The following regression output is for predicting annual murders per million from percentage living in poverty in a random sample of 20 metropolitan areas.

  1. Write the linear model.

\(y =\beta_0 +\beta_1x\)

Annual murders = -29.901 + 2.559 poverty%

  1. Interpret the intercept.

Expected murder rate in metropolitan areas with no poverty (poverty = zero) is -29.901 million.
In this case there is no meaningful value.
The intercept serves to adjust the height of the regression line.

  1. Interpret the slope.
    The slope is responsible for the inclination of the regression line. The angle of the regression line is defined by the slope, \(\theta=arctang \beta_1\).**In this case 2.559 is equivalent to an angle of = 68º39’19.99“.** The practical interpretation is, for each percentage increase in poverty, we expect murders per million to be higher on average by 2.559

  1. Interpret R2.
    R2 of linear model it is also known as the coefficient of determination is one measure of how close are fitted regression line to the data.
    Describes the amount of variation in the response that is explained by the least squares lines (regression model).
    R2 = Explained variation/ Total variation
    Poverty level explain 70.52% of the variability in murder rates in metropolitan areas.

  2. Calculate the correlation coefficient.
    It is simply the square root of R2 \(\sqrt{0.7052}=0.8398\)