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. Conduct a regression analysis at a .05 level of significance. Age of Criminal (X) 32 24 28 17 12 Age of Victim (Y) 24 20 25 22 16 a. What is the critical value? b. Complete the following table. X Y $X - \bar{X}$ $Y - \bar{Y}$ $(X - \bar{X})(Y - \bar{Y})$ $(X - \bar{X})^2$ $(Y - \bar{Y})^2$ 32 24 24 20 28 25 17 22 12 16 $\bar{X} = $ $\bar{Y} = $ $- - $SS_{xy} = $ $SS_x = $ $SS_y = $ c. Complete the F table. Source of Variation Regression Residual Total SS df MS F d. What is your decision? e. What is the regression equation?
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05, we need to find the critical value for a two-tailed test at a 95% confidence level. This can be found using a t-distribution table or a statistical software. For a two-tailed test at a 95% confidence level with 3 degrees of freedom (n-2), the critical value is Show more…
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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 (X): 32, 24, 29, 17, 13 Age of Victim (Y): 24, 21, 26, 23, 17 (a) Compute the method of least squares to find the equation of the regression line. (Round your answers to three decimal places.) Ŷ = ___ 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.) 21.536 years old Refer to steps for computing the method of least squares (Section 16.5).
Ahmet Y.
Q38 Jorge is interested in predicting the number of crimes based on the number of police - officers in a region. Summary statistics for the bivariate data for 12 regions are below. Q50 Figure out which variable is X and which variable is Y, create a regression equation based on these data and then use it to predict. Mean of X: 100 Mean of Y: 20 Sum of (X_i - X̄)": 60 Sum of (X_i - X̄)(Y_i - Ȳ) : 30 Sum of (Y_i - Ȳ)" : 90 Q38 Using the least square criterion, what is the slope of this regression equation? A. 0.2 B. 0.3 C. 0.5 D. 0.22 Q39 Based on the slope you calculated, what is the intercept of this regression equation? A. 30 B. -30 C. 20 D. -20 Q40 Which of the following equations represents the prediction line? A. y_i = ̢β_1x + β_0 + e_i B. y_i = β_1x + β_0 C. ŷ_i = β_1x + β_0 + e_i D. ŷ_i = β_1x + β_0 Q41 Using the regression equation, Jorge obtained the sum of (Y_i - ŷ_i)" = 5. What is the standard error of the slope estimate? A. 0.29 B. 0.09 C. 0.04 D. 0.12 Q42 What is the significance test statistic for the slope estimate? A. 1.74 B. 4.35 C. 11.90 D. 5.55 Q43 Is the slope statistically significant from zero? A. Yes B. No Q44 What is the percentage of the variance in the number of crimes that can be explained by the number of police? A. 0.41 B. 0.17 C. 0.50 D. 0.005 Q45 What is the SS_REGRESSION and SS_error for this regression line, respectively? A. 15.3 and 74.7 B. 74.4 and 15.3 C. 36.9 and 53.1 Q46 What is the significance test statistic for the regression line? A. 1.14 B. 4.57 C. 2.05 D. 3.81 Q47 What is the standard error of the estimate? A. 3.39 B. 2.73 C. 12.59 D. 0.84 Q48 One additional police officer is associated with ____ more crime cases. A. 0.5 B. 0.41 C. 0.84 D. 2
Jerelyn N.
Q. 3 The crime rate was investigated in 50 cities in the U.S.A. (Life In America’s Small Cities, by G.S. Thomas). We are interested in fitting a model for the overall reported crime rate per 1 million residents as a function of the following variables. x1 annual police funding in $/resident x2 % of people 25 years+ with 4 yrs. of high school x3 % of 16 to 19 year-olds not in high school and not high school graduates. x4 % of 18 to 24 year-olds in college x5 % of people 25 years+ with at least 4 years of college a) Fill in the missing values a, b, c, d, e, f, and g in the following ANOVA table. Analysis of Variance Source DF Sum of Squares Mean Square F Value Model a d 282468 g Error b e f Corrected Total c 4233600 b) Perform an ANOVA test at the 1% significance level. c) In two sentences or less: Explain why H0 is rejected when the test statistic used in (b) is large. d) Calculate and interpret the coefficient of determination. e) Here is another ANOVA table which includes results from a model for the overall reported crime rate with only annual police funding and % of people 25 years+ with 4 yrs. of high school (x1 and x2) as covariates. Analysis of Variance Source DF Sum of Squares Mean Square F Value Model 2 1374728 687364 11.30 Error 47 2858872 60827 Corrected Total 49 4233600 Perform a hypothesis test to investigate whether these two variables alone are sufficient to predict the overall reported crime rate per 1 million residents.
Sri K.
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