Question

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

xx	11.7	8.6	6.7	3.3	2.4	2.6	2.2	0.6
yy	14.3	11.1	9.8	6.6	6	6.1	5.8	4.7

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

Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places)

   

A) How many murders per 100,000 residents can be expected in a state with 1.3 thousand automatic weapons?
Answer =  Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 8.9 thousand automatic weapons?
Answer =  Round to 3 decimal places.

Answer 1

The table for regression line equation:

X	y	(x-)	(y-)​​	(x-)2	(x-x)(y-)
11.7	14.3	6.9375	6.25	48.1289	43.3594
8.6	11.1	3.8375	3.05	14.7264	11.7044
6.7	9.8	1.9375	1.75	3.7539	3.3906
3.3	6.6	-1.4625	-1.45	2.1389	2.1206
2.4	6	-2.3625	-2.05	5.5814	4.8431
2.6	6.1	-2.1625	-1.95	4.6764	4.2169
2.2	5.8	-2.5625	-2.25	6.5664	5.7656
0.6	4.7	-4.1625	-3.35	17.3264	13.9444

b) The number of murders per 100,000 residents can be expected in a state with 1.3 thousand automatic weapons is

= 0.86828 × 1.3 + 3.91481 = 5.043574

Therefore, the number of murders per 100,000 residents can be expected in a state with 1.3 thousand automatic weapons is 5.044

C) The number of murders per 100,000 residents can be expected in a state with 8.9 thousand automatic weapons is

= 0.86828 × 8.9 + 3.91481 = 11.643

Therefore, the number of murders per 100,000 residents can be expected in a state with 8.9 thousand automatic weapons is 11.643