# [[EDUC 7215]] final exam Jethro Jones ## Assignment Directions Final Exam (100 points) The dataset used for this final exam was created from a Value-Belief-Norm (VBN) Theory-based survey designed to assess the factors that influence pro-environmental behavior in the Missouri area.  It is the same dataset that you used for your homework assignments.  You will recall that PEB is the arithmetic mean of 20 questions from of the pro-environmental behavior scale developed by Markle (2013).  In previous homework assignments, you analyzed NEP (New Environmental Paradigm), which is the arithmetic mean of 15 questions from the hypothesized facet scale developed by Hawcroft and Milfont (2010), and you also analyzed PN (Personal Norms), which is the arithmetic mean of 9 questions from the personal normative scale developed by Steg et al. (2005).  You also discovered that PEB is influenced by education, which is a nominal scale classification variable with four levels (2 = high school/GED, 3 = associates degree/certificate, 4 = college degree, 5 = masters/PhD/professional degree.  So, we can hypothesize a linear model where PEB is a linear function of NEP, PN, and Education:  PEB = 0 + 1NEP + 2PN + 3Ed2 + 4Ed3 + 5Ed4 + , Where: PEB = Pro-environmental behavior (ratio scale dependent variable), NEP = New Environmental Paradigm (ratio scale independent variable), PN = Personal Norms (ratio scale independent variable), Ed2 = High school diploma or GED (nominal scale independent variable), Ed3 = Associates degree or certificate/license (nominal scale independent variable), Ed4 = Four-year college degree (nominal scale independent variable), 0 - 5 = model parameters to be estimated, and  = residuals that are independent and normally distributed with equal variances. You will recognize that this model is like the model in Assignment 8, except that the nominal scale variable Education replaced the nominal scale variable Gender. Since Education is a classification variable with four levels, we need to add three slopes (3, 4, 5) to the model and use the fourth level (5=masters/PhD/professional degree) as the reference level.  We only needed one slope in the model with Gender from Assignment 8, because Gender only had two levels. For this final exam, use multiple linear regression (MLR) to test if this model describes the relationship between PEB and NEP, PN, and Education.  You will answer the research question, “Is pro-environmental behavior (PEB) a linear function of NEP, PN, and Education for survey respondents in the Missouri area?”  You will need to address the two assumptions of MLR, normality and equal variances of the residuals, through visual assessments of the histogram and Q-Q plots (for normality) and the residual plot (for equal variances).  After you have analyzed the assumptions, you will test the following hypotheses to see if each model parameter (0, 1, 2, 3, 4, 5) differs from zero at the type 1 error rate of 0.05 or 5%. | | | | | | | | --------------------- | --------------------- | --------------------- | --------------------- | --------------------- | --------------------- | | Intercept | Slope of NEP | Slope of PN | Slope of Ed2 | Slope of Ed3 | Slope of Ed4 | | H<sub>0</sub>  0 = 0 | H<sub>0</sub>:  1 = 0 | H<sub>0</sub>:  2 = 0 | H<sub>0</sub>:  3 = 0 | H<sub>0</sub>:  4 = 0 | H<sub>0</sub>:  5 = 0 | | H<sub>a</sub>:  0 ≠ 0 | H<sub>a</sub>:  1 ≠ 0 | H<sub>a</sub>:  2 ≠ 0 | H<sub>a</sub>:  3 ≠ 0 | H<sub>a</sub>:  4 ≠ 0 | H<sub>a</sub>:  5 ≠ 0 | You will also discuss the model fit statistics (RMSE, adjusted R-square) and the Variance Inflation Factors (VIFs). You should also include a Methods paragraph and Summary Statistics for PEB, NEP, and PN by Education. I also recommend that you set the Parameterization of Effects to Reference Coding on the Data tab in SAS, which will help with interpretation of the three slopes for Education (recall that you did this in chapter 13 for classification variables in the binary logistic regression model). For this final exam, you can work together, but I will not be available to answer specific questions or check your results. I will not accept late submissions since it is the end of the semester. The due date for submission is Saturday, May 17, 2025 by 11:59pm. ## Assignment - [ ] MLR to test if this describes relationship between PEB and NEP, PN, and Education. - [ ] Research Question: Is pro-environmental behavior (PEB) a linear function of NEP, PN, and Education for survey respondents in the Missouri area? - [ ] two assumptions of MLR, normality and equal variances of the residuals, visual assessment of - [ ] Histogram and QQ plot (for normality) - [ ] Residual plot (for equal variances) - [ ] Test the hypotheses - [ ] error rate of 0.05 or 5% - [ ] parameterization of effects to reference coding in data tab - [ ] Model fit stats (RMSE, adjusted R-square) - [ ] Variance inflation factors - [ ] Summary stats for PEB, NEP, and PN by education ## Methods I clicked Tasks and Utilities, then Tasks, then Linear Models, then Linear Regression. I selected our work set from my work library. Under Roles, I selected PEB for the dependent variable, Education as the classification variable, and NEP and PN for the continuous variable. Under the Model tab, I selected PN, NEP and education and add. In options, I selected Individual plots for both the diagnostic and residual plots. After I clicked Run, I opened it in a new tab and saved the graphs and took screenshots as you'll see below. I used an AI renaming tool to rename the screenshots and graphs appropriately. I then used Tasks and Utilities, then Tasks, then Statistics, then Summary Statistics to generate summary statistics for PEB and NEP, PN and Education. Under Option, then Basic Statistics, I check Mean, Standard Deviation, minimum Value, Maximum Value and Median. Under Additional Statistics, I checked 95% Confidence Limits for the mean. Under Plots, I notched the Comparative box plot. After I clicked Run, I opened it in a new tab and saved the graphs and took screenshots as you'll see below. I used an AI renaming tool to rename the screenshots and graphs appropriately. Here are my screenshots from SAS ![[2025-05-05 SAS_Studio_Regression_Analysis-KO3ei5e9KO.png]] ![[2025-05-05 SAS_Model_Effects_Builder.png]] ![[2025-05-05 SAS_Studio_Interface.png]] ![[2025-05-05 SAS_Studio_Statistical_Analysis.png]] ![[2025-05-05 SAS_Studio_Regression_Analysis.png]] ## Graphs and Tables ![[2025-05-05 Statistical Summary Table.png]] ![[2025-05-05 Distribution of PN by education.png]] ![[2025-05-05 Distribution of NEP by education.png]] ![[2025-05-05 Distribution of PEB by education.png]] ![[2025-05-05 DataSetSummary-SeealeRQuT.png]] ![[2025-05-05-Least-Squares-Summary.png]] ![[2025-05-05_Least_Squares_Model_Analysis.png]] ![[2025-05-05_Model1_ParameterEstimates_CollinearityDiagnostics.png]] ![[2025-05-05 Distribution of Residuals for PEB.png]] ![[2025-05-05 Residuals_Predicted_PEB.png]] ![[2025-05-05 RStudent Predicted PEB Scatterplot.png]] ![[2025-05-05 Observed_vs_Predicted_PEB_Scatterplot.png]] ![[2025-05-05 CooksDPlot.png]] ![[2025-05-05 Outlier Leverage Diagnostics PEB.png]] ![[2025-05-05 QQPlotResidualsPEB.png]] ![[2025-05-05 ResidualFitSpreadPlotPEB.png]] ![[2025-05-05 ResidualsForPEBScatterPlot.png]] ![[2025-05-05 ResidualsForPEBScatterPlot-KTl_foLDxr.png]] ![[2025-05-05 ResidualsForPEB.png]] ![[2025-05-05 ResidualsForPEB-vK4TxUeT6G.png]] ![[2025-05-05 Residuals_for_PEB.png]]