Question

1. An instructor measured quiz scores and the number of hours studying among a sample of 20 college students. If SSXY = 44, SSX = 98, MY = 6, and MX = 4, then what is the regression equation for this sample? (Round your numerical values to three decimal places.)
= _______ X +________

2. 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	20
29	25
17	22
13	17

(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 24 years old. (Round your answer to three decimal places.)

Answer 1

1) since

SSx = 98,SSxy= 44

My= 6,Mx= 4. n= 20

So

Slope = b = SSxy/SSx = 44/98 = 0.449

Intercept = a= My-bMx . = 6-0.449×4 = 4.204

So regression equation

Y^ = 4.204+0.449x

2)

X	y	(x-xbar)^2	(y-ybar)^2
32 24 29 17 13 M: 23	25 20 25 22 17 M: 21.8	81 1 36 36 100 SS: 254	28.8 -1.8 19.2 -1.2 48 SP: 93

Regression

Sum of X = 115
Sum of Y = 109
Mean X = 23
Mean Y = 21.8
Sum of squares (SSX) = 254
Sum of products (SP) = 93

Regression Equation = ŷ = bX + a

b = SP/SSX = 93/254 = 0.366

a = MY - bMX = 21.8 - (0.366*23) = 13.382

ŷ = 0.366X + 13.382

b) when x=24

Y^ = 22.166