Question

1. A regression analysis was performed to determine if there is a relationship between hours of TV watched per day (xx) and number of sit ups a person can do (yy). The results of the regression were:

y=ax+b
a=-1.072
b=31.456
r2=0.859329
r=-0.927

Use this to predict the number of sit ups a person who watches 8 hours of TV can do, and please round your answer to a whole number.

2.

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

xx	11.5	8.4	6.6	3.4	2.6	2.2	2.7	0.9
yy	13.9	11.2	9.6	6.9	5.9	6.1	6.5	5.1

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 5.7 thousand automatic weapons?
Answer =  Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 7.9 thousand automatic weapons?
Answer =  Round to 3 decimal places.

Answer 1

1)

y = ax + b

y = -1.072x + 31.456

when x = 8

y = -1.072 * 8 + 31.456

y = 23

2)

X	Y	XY	X^2	Y^2
11.5	13.9	159.85	132.25	193.21
8.4	11.2	94.08	70.56	125.44
6.6	9.6	63.36	43.56	92.16
3.4	6.9	23.46	11.56	47.61
2.6	5.9	15.34	6.76	34.81
2.2	6.1	13.42	4.84	37.21
2.7	6.5	17.55	7.29	42.25
0.9	5.1	4.59	0.81	26.01

n	8
sum(XY)	391.65
sum(X)	38.30
sum(Y)	65.20
sum(X^2)	277.63
sum(Y^2)	598.70

a	0.84
b	4.11

ycap = ax + b

ycap = 0.84x + 4.11

a)

x = 5.7

ycap = 0.84 * 5.7 + 4.11

ycap = 8.898

b)

x = 7.9

ycap = 0.84 * 7.9 + 4.11

ycap = 10.746