Question

17. (-/3 Points) DETAILS PRIVITERASTATS3 16.8.019. MY NOTES PRACTICE ANOTHER A forensic psychologist tests the extent to which the age of a criminal (X) predict the age of the victim (Y) for nonviolent crimes. The paychologist uses the cases 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 Y X 25 33 24 20 25 25 22 13 16 (a) Compute the method of least squares to find the equation of the regression line. (Round your answers to three decimal places.) Y (b) Use the regression equation to determine the predicted age of a victim of a nonviolent crime when the criminalis 20 years old. (Round your answer to three decimal places) years old Additional Materials

Answer 1

Solution Given Criminal Age of Age of Victim X у 33 25 20 24 25 28 22 18 16 13 (a) To compute the method of least squares to find the equation of the regression line 2 2 X Y ху у 625 825 1089 33 25 480 20 576 400 24 625 784 700 28 29 396 324 484 18 169 256 208 16 13 2 2 Y= 108 Eny = 2609 2x = 2942 Y = 2390 [x = 116

* Now to calculate slope (b) b= hsxy - (2x)(59) nex² - ({x)? b= 5(269) - (116) (108) 5 (2942) - (116) b 13045-12528 14710-13456 b= 517 1254 b = 0.412 intercept, (a): * Now to calculate the Eybex a 108 - 0.412 (116) 5 108 - 47.792 60.208 5 a = 12.042 (a=12.042

ŷ = bxta = 0.412 x + 12.042 10.412 x + (12.042 by (6) The gregression equation is given 4 y = 0.412x + 12.042 0 Now to substitute the x=20 in equation ③ then we get ŷ = 0.412 (20) + 12.042 ý = 8.24 + 12.042 20.282 ..ŷ - 20.282 Years old Hence the predicted age of a nonvident crime when the criminal is 20 years old is 20.282