The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.
x | 11.6 | 8 | 6.7 | 3.7 | 2.6 | 2.6 | 2.3 | 0.5 |
---|---|---|---|---|---|---|---|---|
y | 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
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