Question

You have the following regression equation for the effect of streetlights per block (x) on crimes per month (y): y = 2.4 -0.2x. Calculate the residual for a block with 10 streetlights and 1 crime a month (10,1).

A. -1.2
B. 0.6
C. 0.4
D. -0.6

Answer 1

The residual for a block with 10 streetlights and 1 crime a month is 0.6. This is calculated by predicting the crimes using the regression equation and then subtracting the predicted value from the observed value.

Step-by-step explanation:

To calculate the residual for the given regression equation y = 2.4 - 0.2x for a block with 10 streetlights and 1 crime a month, we first use the regression equation to predict the number of crimes for a block with 10 streetlights. Substituting x with 10, the predicted crimes would be y = 2.4 - 0.2(10) = 2.4 - 2 = 0.4.

The residual is the difference between the observed and predicted values. The observed number of crimes is 1, so the residual would be 1 - 0.4 = 0.6. Hence, the calculated residual is 0.6, which matches with option B.