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Psychological Statistics Laboratory 10 Regression Analysis Case 1. A neuroscientist suspects that low levels of the brain neurotransmitter serotonin may be causally related to aggressive behavior. As a first step in investigating this hunch, she decides to do a correlative study involving nine rhesus monkeys. The monkeys are observed daily for 6 months, and the number of aggressive acts is recorded. Serotonin levels in the striatum (a brain region associated with aggressive behavior) are also measured once per day for each animal. The resulting data are shown below. The number of aggressive acts for each animal is the average for the 6 months, given on a per-day basis. Serotonin levels are also average values over the 6-month period. Serotonin Level Number of Aggressive (microgm/gm) Acts/day 0.32 6.0 0.35 3.8 0.38 3.0 0.41 5.1 0.43 3.0 0.51 3.8 0.53 2.4 0.60 3.5 0.63 2.2 A. What is your predictor variable, what is the criterion variable? B. What is the appropriate regression technique to use and why? C. Make an APA table and write an interpretation for Regression and implication/inference. Model Summary Model R .637a 1 R Square Adjusted R Square .405 Std. Error of the Estimate .320 1.01817 a. Predictors: (Constant), Serotonin ANOVAa Model 1 Sum of Squares Regression Residual Total df Mean Square 4.946 7.257 1 7 12.202 8 4.946 1.037 F Sig. 4.771 .065b a. Dependent Variable: Aggression b. Predictors: (Constant), Serotonin Coefficientsa Model Unstandardized Coefficients B 1 (Constant) Serotonin Std. Error 6.939 -7.127 1.546 3.263 Standardized Coefficients Beta -.637 t 4.488 -2.184 Sig. .003 .065 a. Dependent Variable: Aggression Case 2. A statistics professor conducts a study to investigate the relationship between the performance of his students on exams and their anxiety. Ten students from his class are selected for the experiment. Just before taking the final exam, the 10 students are given an anxiety questionnaire. Here are final exam and anxiety scores for the 10 students. A. What is your predictor variable, what is the criterion variable? B. What is the appropriate regression technique to use and why? C. Make an APA table and write an interpretation for Regression and implication/inference. Model Summary Model R .691a 1 R Square Adjusted R Square .477 Std. Error of the Estimate .412 10.86532 a. Predictors: (Constant), Anxiety ANOVAa Model 1 Sum of Squares Regression Residual Total df Mean Square 861.959 944.441 1 8 1806.400 9 861.959 118.055 F Sig. 7.301 .027b a. Dependent Variable: Final exam score b. Predictors: (Constant), Anxiety Coefficientsa Model Unstandardized Coefficients B 1 (Constant) Anxiety 125.883 -1.429 a. Dependent Variable: Final exam score Std. Error 21.111 .529 Standardized Coefficients Beta -.691 t 5.963 -2.702 Sig. .000 .027 APA SAMPLE ON REGRESSION (LINEAR) A clinical psychologist is interested in the relationship between testosterone level in married males and the quality of their marital relationship. A study is conducted in which the testosterone levels of eight married men are measured. The eight men also fill out a standardized questionnaire assessing quality of marital relationship. The questionnaire scale is 0 – 25, with higher numbers indicating better relationships. Testosterone scores are in nanomoles/liters of serum. The data are shown below. A. What is your X (predictor) variable, what is Y (criterion) variable? Predictor=Testosterone, Criterion=Marital relationship quality/Quality of marital relationship B. What is the appropriate regression technique to use and why? Simple linear regression C. Make an APA table and write an interpretation for Regression (indicate if your X variable significantly predicts your Y variable). Model Summary Model R R Square .562a 1 Adjusted R Square .316 Std. Error of the Estimate .202 4.24199 a. Predictors: (Constant), Testosterone ANOVAa Model 1 Sum of Squares df Mean Square Regression Residual 49.908 107.967 1 6 Total 157.875 7 F 49.908 17.995 Sig. .147b 2.774 a. Dependent Variable: Relationship b. Predictors: (Constant), Testosterone Coefficientsa Model Unstandardized Coefficients B (Constant) Testosterone 1 Std. Error 24.964 -.513 Standardized Coefficients Beta 5.227 .308 t Sig. 4.776 -1.665 -.562 .003 .147 a. Dependent Variable: Relationship Table 5 Predictor of marital relationship Model 1 Predictor Variable Testosterone R R2 F ß p .562 .316 2.774 -.513 .147 Verbal Interpretation Not Significant ***p<.001, **p<.01 Table 5 shows the predictor of marital relationship. The correlation indicates an inverse moderate relationship and the regression describes the total variance of marital relationship by 31.6%. However, the model implied that Testosterone did not significantly predict marital relationship quality, F (1, 6) = 2.774, ß= -0.513, p=.147. The implication of this is that whatever level of testosterone the married man has does not affect their marital relationship if they become happier or not.