Question

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.

xx	11.5	8.4	6.9	3.9	2.9	2.8	2.6	0.9
yy	14.1	10.9	10.1	7.5	6.4	6.6	6.1	5

xx = thousands of automatic weapons
yy = murders per 100,000 residents

This data can be modeled by the linear equation

ˆy=0.86x+4.07y^=0.86x+4.07

1. How many murders per 100,000 residents can be expected in a state with 9.2 thousand automatic weapons? Round to 3 decimal places.
   
   murders per 100,000 residents
   
2. How many murders per 100,000 residents can be expected in a state with 3.8 thousand automatic weapons? Round to 3 decimal places.
   
   murders per 100,000 residents

Answer 1

Solution:
Given in the question
Predicted regression equation is
Y^ = 0.86*X + 4.07
Here X is thousand automatic weapons
Y is murders per 100,000 residents
Solution(a)
Given X = 9.2 thousand, we need to calculate Y
Y^ = 0.86*X + 4.07 = 0.86*9.2 + 4.07 = 11.982 murders per 100,000 residents
11.982 murders per 100,000 residents can be expected in a state with 9.2 thousand automatic weapons.
Solution(b)
Given X = 3.8 thousand, we need to calculate Y
Y^ = 0.86*X + 4.07 = 0.86*3.8 + 4.07 = 7.338 murders per 100,000 residents
7.338 murders per 100,000 residents can be expected in a state with 3.8 thousand automatic weapons.