Question

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

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

 xx yy 11.5 8.4 6.9 3.9 2.9 2.8 2.6 0.9 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

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.

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