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.

 x y 11.6 8 6.7 3.7 2.6 2.6 2.3 0.5 14.1 10.6 9.7 7 6.4 6.1 6 4.5

x = thousands of automatic weapons
y = murders per 100,000 residents

This data can be modeled by the equation y=0.86x+3.98. Use this equation to answer the following;
Special Note: I suggest you verify this equation by performing linear regression on your calculator.

A) How many murders per 100,000 residents can be expected in a state with 2.3 thousand automatic weapons?

Answer =  Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 8.5 thousand automatic weapons?

Answer =  Round to 3 decimal places.

Sum of X = 38
Sum of Y = 64.4
Mean X = 4.75
Mean Y = 8.05
Sum of squares (SSX) = 95.7
Sum of products (SP) = 81.9

Regression Equation = ŷ = bX + a

b = SP/SSX = 81.9/95.7 = 0.86

a = MY - bMX = 8.05 - (0.86*4.75) = 3.98

ŷ = 0.86X + 3.98

A. For x=2.3, ŷ = (0.86*2.3) + 3.98= 5.958

B. For x=8.5, ŷ = (0.86*8.5) + 3.98=11.290