Question

# 1. A regression analysis was performed to determine if there is a relationship between hours of...

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 yy 11.5 8.4 6.6 3.4 2.6 2.2 2.7 0.9 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.

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) 38.3 sum(Y) 65.2 sum(X^2) 277.63 sum(Y^2) 598.7
 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

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