Question

A. Here is a bivariate data set.

x	y
73	47
81	19
76	11
72	83
55	86
67	25
64	76
66	77
72	-3
62	55

Find the correlation coefficient and report it accurate to four decimal places.
r =

B.

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

xx	11.5	8	7.1	3.7	2.5	2.7	2.3	0.5
yy	13.7	11	10.1	7.2	6	6.5	6.2	4.4

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

This data can be modeled by the equation y=0.85x+4.09.y=0.85x+4.09. 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 4.1 thousand automatic weapons?

Answer =  Round to 3 decimal places.

b) How many murders per 100,000 residents can be expected in a state with 1.7 thousand automatic weapons?

Answer =  Round to 3 decimal places.

C.

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=-1.314 b=34.695 r²=0.603729 r=-0.777 Use this to predict the number of sit ups a person who watches 1.5 hours of TV can do, and please round your answer to a whole number.

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
73	47	17.64	0.360	-2.52
81	19	148.84	817.960	-348.92
76	11	51.84	1339.560	-263.52
72	83	10.24	1253.160	113.28
55	86	190.44	1474.560	-529.92
67	25	3.24	510.760	40.68
64	76	23.04	806.560	-136.32
66	77	7.8400	864.3600	-82.3200
72	-3	10.240	2560.360	-161.920
62	55	46.240	54.760	-50.320

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	688	476	509.600	9682.40	-1421.8
mean	68.80	47.60	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) = -1421.8/√(509.6*9682.4) = -0.6401

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B)

a)  
y=0.85x+4.09  
x=4.1  
y=0.85*4.1+4.09=   7.575
  
b)  
y=0.85x+4.09  
x=1.7  
y=0.85*1.7+4.09=   5.535
  
  
C  
y=-1.314*x + 34.695  
x=1.5  
y=-1.314*1.5 + 34.695=   33