A forensic psychologist tests the extent to which the age of a criminal (X) pred

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 les 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. (a) Compute the method of least squares to find the equation of the regression line. (Round your answers to three decimal places.) (b) Use the regression equation to determine the predicted age of a victim of a nonviolent crime when the criminal is 23 years old. years old

Explanation / Answer

HEre we will use least square regression method by evaluting values of x2 , y2 and xy. The table is given below.

As the linerar regression line equation is

y^ = a + b X

so here a =  [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

a = [ 111 * 2874 - 114 * 2621] / [ 5 * 2874 - 1142 ]

a = 20220/ 1374 = 14.72

b =  [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [ 5 * 2621 - 114 * 111] / [ 5 * 2874 - 1142 ]

b = 451/ 1374 = 0.328

so linear regression line is

y^ = 14.72 + 0.328 x

so if age of criminal is 23 so predicted age if victim is

y^ = 14.72 + 0.328 * 23 = 22.26 years.

X Y X^2 Y^2 XY 32 24 1024 576 768 24 21 576 441 504 29 26 841 676 754 17 23 289 529 391 12 17 144 289 204 Total 114 111 2874 2511 2621

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