Question

A forensic psychologist tests the extent to which the age of a criminal (X) predicts the age of the victim (Y) for nonviolent crimes. The psychologist uses the case files to record the age of five criminals and the age of the victim in those cases. The hypothetical data are listed in the following table.

Age of Criminal	Age of Victim
X	Y
32	25
24	21
28	25
17	23
12	16

(a) Compute the method of least squares to find the equation of the regression line. (Round your answers to three decimal places.)
=  X +  

(b) Use the regression equation to determine the predicted age of a victim of a nonviolent crime when the criminal is 20 years old. (Round your answer to three decimal places.)

Answer 1

Solution :

X	Y	XY	X^2	Y^2
32	25	800	1024	625
24	21	504	576	441
28	25	700	784	625
17	23	391	289	529
12	16	192	144	256

n	5
sum(XY)	2587.00
sum(X)	113.00
sum(Y)	110.00
sum(X^2)	2817.00
sum(Y^2)	2476.00
Numerator	505.00
Denominator	607.03
r	0.8319
r square	0.6921
Xbar(mean)	22.6000
Ybar(mean)	22.0000
SD(X)	7.2553
SD(Y)	3.3466
b	0.3837
a	13.3275

(a)

Y = 0.384 X + 13.328

(b)

Y = 0.3837 * 20 + 13.3275 = 21.002

Predicted age = 21.002