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 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 33   24 24   21 28   25 17   22 12   16
(a) Compute the method of least squares to find the equation of the regression line. (Round your answers to three decimal places.) Y hat =____x +______

(b) Use the regression equation to determine the predicted age of a victim of a nonviolent crime when the criminal is 23 years old. (Round your answer to three decimal places.)    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 33   24 24   21 28   25 17   22 12   16
(a) Compute the method of least squares to find the equation of the regression line. (Round your answers to three decimal places.) Y hat =____x +______

(b) Use the regression equation to determine the predicted age of a victim of a nonviolent crime when the criminal is 23 years old. (Round your answer to three decimal places.)    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 33   24 24   21 28   25 17   22 12   16
(a) Compute the method of least squares to find the equation of the regression line. (Round your answers to three decimal places.) Y hat =____x +______

(b) Use the regression equation to determine the predicted age of a victim of a nonviolent crime when the criminal is 23 years old. (Round your answer to three decimal places.)   

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Y
Independent Variable: X
Y = 13.570014 + 0.35219236 X
Sample size: 5
R (correlation coefficient) = 0.84437834
R-sq = 0.71297478
Estimate of error standard deviation: 2.1696114

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) Regression equation will be:

y hat = 0.352 x + 13.570

b) For x = 23,

y hat = 0.352*23 + 13.570 = 21.666

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 13.570014 3.0974495 0 3 4.3810284 0.022 Slope 0.35219236 0.12901561 0 3 2.7298431 0.072

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