Rubric posted at the end of this document
Assume that the DV distribution is appropriate for regression (unless you are asked to evaluate it). You do not have to test regression assumptions, except insofar as the questions below specifically ask you to. Data are in Class12_homework_2022.sav.
Smith, Fuimaono, and Ioane (2020) collected data from 1000 community-dwelling younger adults. The DV was Dopaminergic Signaling, taken from a continuous measure of dopamine concentration throughout the study visit, assessed via implanted fiber optic cable. Two variables were used to predict dopaminergic signalling: (1) amount of high-intensity physical activity; and (2) emotion processing speed. Higher levels represent more of the named trait (for processing speed, higher has been coded to mean -faster-). The metric on each of these variables is may be a bit unusual; don’t worry about this, as it represents rescales commonly done in this lab.
1. [__/10] Run the following regression: Dopaminergic signalling = high intensity physical activity + emotion processing speed. Briefly summarize the results.
2. [__/10] It turns out that the dopaminergic signaling DV is a bit platykurtic, and a purist colleague argues that we shouldn’t have run the above regression. As an appeasement step, rerun the regression in #1 as a robust (bootstrapped) regression, winsorizing the DV (20% trimmed mean) and using 1,000 bootstrap samples. Summarize your results; is the pattern of results similar to #1? You do not need to compute standardized betas. Note. As in the in-class assignment, R is not reading the DV as numeric, so you have to fix this before running the winsorization:
#Note: For reasons I cannot understand, R does not interpret
#dopa as a numeric variable.
#To make the winsorization work, you first have to explicitly
#code dopa as numeric
#See next step.
Wk12$dopa -as.numeric(Wk12$dopa)
#You can then use your psych::winsor statement on dopa
3. [__/10] Returning to the original (unwinsorized) version of the DV, ignoring the poor distribution, it turns out that high intensity physical activity and emotion processing speed interact. Test the regression: Dopaminergic signalling = high intensity physical activity + emotion processing speed + (high intensity physical activity*emotion processing speed), using mean-centered main effects and Aiken and West mean-centering for the interaction. Please plot the interaction graphically as well.
Rubric
Q1
10-point 9-point 8-point 7-point 0-point
? Conducting stated regression
? Providing the following output for the lm: summary(), lm.beta()
? Evaluating the model according to the following conventional criteria: R-squared and associated omnibus test; b/beta/p-value (significance/ direction/ magnitude) of all predictors
o Please be certain to include the following results in your written summary: total variance explained by the model (R-squared), omnibus results (F, degrees of freedom, and p-values) along with standardized/ unstandardized betas and p-values for each predictor
? Example: [F(2,150)=14.534, p = or .05); (b=4.58, B=5.01, p = or .05)
o Also, please be certain to explain the amount of unit increase or decrease in the DV that is associated with each significant predictor, along with talking about relative magnitude and direction of EACH predictor
? When reporting magnitude, please be specific about which effect size conventions you are using. Missing one or two elements of a #10 answer. Commonly this means incomplete reporting of statistics, or incomplete narrative. May be substantially a “10” or “9” answer, but there is at least one computation or setup error that results in one or more incorrect numbers. All elements of the answer may be excellent, but the answer is “wrong” due to incorrect computations/calculations. Alternatively, an “8” could indicate an answer that is simply missing more elements than a “9” answer (e.g., 3+ elements), but the answer is correct enough to warrant higher than a “7”. “mercy point” (e.g., you really don’t deserve a point, but because you made some attempt, this is acknowledged; example: doing a “descriptives” when the question can only be fulfilled by a “frequencies”, dumping output but no interpretation) No response, or you put the wrong output [e.g., for the wrong question] in your answer. Evidence of minimal effort or attention.

Q2
10-point 9-point 8-point 7-point 0-point
? Rerunning the regression in #1 as a robust regression, winsorizing the DV and using 1,000 bootstrap samples
? Providing the following output for the regression: bootstrapped coefficient/bias//standard error for b-weights and r-squared; bootstrapped bca confidence intervals for b-weights and r-squared.
? Evaluating the model according to the following conventional criteria: R-squared and associated omnibus test; b/p-value (significance/ direction) of all predictors
o Please be certain to include the following results in your written summary: total variance explained by the model (R-squared), omnibus results (F, degrees of freedom, and p-values) along with unstandardized betas and p-values for each predictor
? Example: [F(2,150)=14.534, p = or .05); (b=4.58, p = or .05)
? Discussing how the results of this model compare to the results of the model from #1 (e.g., variance explained, significance/direction of predictors) Missing one or two elements of a #10 answer. Commonly this means incomplete reporting of statistics, or incomplete narrative. May be substantially a “10” or “9” answer, but there is at least one computation or setup error that results in one or more incorrect numbers. All elements of the answer may be excellent, but the answer is “wrong” due to incorrect computations/calculations. Alternatively, an “8” could indicate an answer that is simply missing more elements than a “9” answer (e.g., 3+ elements), but the answer is correct enough to warrant higher than a “7”. “mercy point” (e.g., you really don’t deserve a point, but because you made some attempt, this is acknowledged; example: doing a “descriptives” when the question can only be fulfilled by a “frequencies”, dumping output but no interpretation) No response, or you put the wrong output [e.g., for the wrong question] in your answer. Evidence of minimal effort or attention.

Q3
10-point 9-point 8-point 7-point 0-point
? Conducting the regression in #1 again, this time including the stated interaction, and using mean-centered main effects and Aiken and West mean-centering for the interaction.
? Providing the following output for the regression: for the lm: summary(), lm.beta(), as well as the interaction plot_model visualization
? Evaluating the model according to the following conventional criteria: R-squared and associated omnibus test; b/beta/p-value (significance/ direction/ magnitude) of all predictors and the interaction
o Please be certain to include the following results in your written summary: total variance explained by the model (R-squared), omnibus results (F, degrees of freedom, and p-values) along with standardized/ unstandardized betas and p-values for each predictor and the interaction
? Example: [F(2,150)=14.534, p = or .05); (b=4.58, B=5.01, p = or .05)
o Also, please be certain to explain the amount of unit increase or decrease in the DV that is associated with each significant predictor, along with talking about relative magnitude and direction of EACH predictor
? When reporting magnitude, please be specific about which effect size conventions you are using.
? Summarizing what the interaction plot tells you about the interaction (i.e., what do the different lines in the plot tell you about the nature of this specific interaction?) Missing one or two elements of a #10 answer. Commonly this means incomplete reporting of statistics, or incomplete narrative. May be substantially a “10” or “9” answer, but there is at least one computation or setup error that results in one or more incorrect numbers. All elements of the answer may be excellent, but the answer is “wrong” due to incorrect computations/calculations. Alternatively, an “8” could indicate an answer that is simply missing more elements than a “9” answer (e.g., 3+ elements), but the answer is correct enough to warrant higher than a “7”. “mercy point” (e.g., you really don’t deserve a point, but because you made some attempt, this is acknowledged; example: doing a “descriptives” when the question can only be fulfilled by a “frequencies”, dumping output but no interpretation) No response, or you put the wrong output [e.g., for the wrong question] in your answer. Evidence of minimal effort or attention.