Statistics for the Behavioral Sciences
Statistics for the Behavioral Sciences
2nd Edition
ISBN: 9781452286907
Author: Gregory J. Privitera
Publisher: SAGE Publications, Inc
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Chapter 16, Problem 19CAP

(a)

To determine

Find the equation of the regression line.

(a)

Expert Solution
Check Mark

Answer to Problem 19CAP

The equation of the regression line is, Y^=0.36X+13.17.

Explanation of Solution

Calculation:

The information given that is the case files to record the age of five criminals and the age of the victim in those cases with the factors age of a criminal (X) predicts the age of the victim (Y) for nonviolent crimes.

The procedure of straight line by using the method of least square is shown below:

  • Compute preliminary calculations.
  • Calculate the slope (b).
  • Calculate the y-intercept (a).

The formula for slope is,

slope(b)=SSXYSSX

Where,

SSXY=(XMX)(YMY)

SSX=(XMX)2

In the formulas, MX denotes the mean of factor X, MY denotes the mean of factor Y.

The formula for y-intercept is,

a=MYbMX

The regression equation is, Y^=bX+a.

The value of SSX:

The value of mean for X is,

MX=32+24+28+17+125=1135=22.6

XY(XMX)(XMX)2
3224(3222.6)=9.488.36
2420(2422.6)=1.41.96
2825(2822.6)=5.429.16
1722(1722.6)=5.631.36
1216(1222.6)=10.6112.36
(XMX)2=263.2

Table 1

The value of SSX is 263.2.

The value of SSXY:

The value of mean for Y is,

MY=24+20+25+22+165=1075=21.4

XY(XMX)(XMY)(XMX)(XMY)
3224(3222.6)=9.4(2421.4)=2.624.44
2420(2422.6)=1.4(2021.4)=1.4–1.96
2825(2822.6)=5.4(2521.4)=3.619.44
1722(1722.6)=5.6(2221.4)=0.6–3.36
1216(1222.6)=10.6(1621.4)=5.457.24
(XMX)(XMY)=95.8

Table 2

The value of SSXY is 95.8.

Slope:

Substitute, SSX=263.2 and SSXY=95.8 in slope formula

slope(b)=95.8263.2=0.364

Hence, the value of slope is 0.364.

Substitute, MY=21.4,MX=22.6,b=0.364 in y-intercept formula.

a=MYbMX=21.4(0.364)22.6=21.48.2264=13.174

Hence, the value of y-intercept is 13.174.

Substitute, a=13.174,b=0.364 in regression equation formula.

Y^=(0.364)X+13.174=0.36X+13.17

The equation of the regression line is, Y^=0.36X+13.17.

(b)

To determine

Find the predicted age of a victim of a nonviolent crime when the criminal is 20 years old.

(b)

Expert Solution
Check Mark

Answer to Problem 19CAP

The predicted age of a victim of a nonviolent crime when the criminal is 20 years old is 20.37 years old.

Explanation of Solution

Calculation:

The given information is that the criminal is 20 years old.

The equation of the regression line is Y^=0.36X+13.17.

Substitute, X=20 in regression line.

Y^=0.36(20)+13.174=7.2+13.17=20.37

Hence, the predicted age of a victim of a nonviolent crime when the criminal is 20 years old is 20.37 years old.

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