PART I: Regression Model Diagnostics
For this part, you will use dataset grit study along with the codebook for the data if needed. (If you have a dataset of your own that you prefer to use for this assignment, please consult the instructor for prior approval. To determine whether your dataset is appropriate for this assignment, you will be asked to submit a description of the dataset and information about the variables you wish to analyze, including the measurement scales and basic descriptive data such as means and standard deviations.)
Run a standard simultaneous regression analysis, regressing college students' achievement (Grade1) on the following variables treated as predictors (sex, ethnicity, grit, and constructs 1 to 6). Don't forget to treat properly qualitative variables before carrying out the multiple regression analysis. Simultaneously elicit appropriate diagnostic information to check regression assumptions, multi-collinearity, outliers, leverage, and influence. Paste relevant diagnostic information from the output in answering each of the questions below.
1. Examine the assumptions of normality, linearity, and homoscedasticity through plots and any formal/informal statistical testing or information.
(a) Plot the histogram of standardized residuals and indicate outliers if there is any along with your criterion. Discuss if normality of residual assumption is approximately satisfied or not.
(b) Generate P-P and Q-Q plots of standardized residuals, and comment about normality assumption for the current model.
(c) Plot standardized residuals (Y axis) vs predicted science score (X axis), and comment about linearity and homoscedasticity assumption.
(d) Plot standardized residuals (Y axis) vs each predictor (X axis), and discuss which plots (predictors) can be potentially problematic in the context of linearity and homoscedasticity assumptions. Note that you can use original categorical variables for these plots.
(e) Consider transformations to address problems you found. If you decide that transformations are appropriate, re-run the regression analysis using the transformed variables and report and interpret the results. Be sure to include and discuss all relevant graphs, plots, and tables for parts (a), (b), (c), and (d). If your decision is not to transform any of the variables, defend your decision with proper supporting details.
2. Examine multicollinearity diagnostic information for the current model. (If you transformed some variables, the current model is the new model with transformed variables. If you decided not to transform any variables, the current model is the same as the first model you ran)
(a) Identify and report problematic predictors including the values of diagnostic indices.
(b) Explain why the identified predictors are problematic including what effects of multi-collinearity are.
(c) Explain how you can address the multicollinearity problem that you found and carry out the remedy action that you choose among them. Be sure to examine the issue again and report the results after your action.
3. Examine outliers, leverage, and influence of the current model after you addressed multi-collinearity problem.
(a) Based on the outlier information, what do you conclude about potential outliers? Use a justifiable cutoff for the appropriate analysis of residuals.
(b) Determine (calculate) and apply the leverage cutoff as shown in class for leverage values.
What conclusion do you make concerning the existence of any potential outliers in the data in terms of the predictors? Which case(s) is (are) suspect?
(c) Determine which, if any, cases are unduly influencing the regression. Use Cook's D and standardized DFBETA values to make your determination. State what criteria you used to make your decisions.
(d) Summarize your findings from questions (a), (b), and (c), and explain how your diagnostic information (graphical and numerical) led you to your conclusions. If you identified any outliers on y or the x's (from question (a) above) or influential points (from question (b) and (c) above), state those case(s) (students) and remove them from your data, under the assumption that there was good theoretical reason, and return the subsequent regression analysis. If no aberrant cases are present, just use the information you have to answer the remaining questions.
(e) Rerun the regression now based on a model with aberrant cases deleted. If no cases were identified and deleted from the diagnostic work above, then use the previous regression model from the most recent model above, what conclusions do you draw about the normality of residuals assumption?
(f) Examine normality, linearity, homoscedasticity assumptions one more time for your final model and report the results.
4. Write-up
Assume that you are a researcher who is interested in two primary research questions as follows:
(a) Do the set of predictors account for a significant proportion of variance in score variable (grade1)?
(b) Does each predictor have a significant influence on score variable (grade1), controlling for other variables in the model?
Provide the appropriate SPSS or R output to answer these questions and write-up the results (from the final model) using the statistical write-up notes as a guide (or template). Tables and figures should be properly formatted. Please include your analysis results about model diagnostics (assumptions, multicollinearity, outliers, leverage, and influences) in your writing after addressing the research questions. Do not forget to include confidence intervals and/or effect sizes as part of your write-up.
Note: As I did not ask to drop insignificant predictors for this assignment, the final model could include statistically insignificant predictors.
PART II: Journal Article Review
In this part of assignment you will read an assigned article that reports the results of one or more multiple regression analyses. The purpose of this assignment is to interpret and critique the regression analyses (particularly for a moderator effect) performed in this article. What I expect is a critique paper that should address the following points:
1. Briefly describe the purpose and procedures of the study and the variables analyzed. What are the research questions as they pertain to the regression analyses? Identify the dependent and independent variables.
2. Briefly describe the sample data used (who was included in the sample?), the sample size, how the sample was selected, and the intended population of generalization. Use that information to comment on the adequacy of the sample size for the analyses performed, and the representativeness of the sample for the intended population of generalization.
3. Describe the regression analyses performed in the paper.
4. Interpret the results of the regression analyses performed in the paper.
5. Discuss whether the (regression-related) conclusions drawn in the paper follow from the regression analyses reported.
6. Discuss the extent to which the authors tested and/or addressed the assumptions underlying multiple regressions.
7. Discuss weaknesses or problems with the analyses reported in the paper and describe alter-native analyses that could have, or should have, been performed. If the authors did not test or address the assumptions underlying multiple regression, what are some potential weakness or problems with their quantitative analyses? What analyses should be performed to address these assumptions?
Note 1: In addition to conventional regression analyses, the article may contain analyses that have not been discussed in EDMS 645, 646, and 651(e.g., matching technique, hierarchical or multilevel modeling). You do not need to discuss or critique these analyses technically but still can evaluate the approach conceptually (if you want).
Note 2: There is no limit in terms of length, but this part of assignment typically ends up with approximately 2-3(single-spaced) pages.
PART III: Weighted Least Squares Regression
You can earn up to 3 points by completing this part depending on the level of performance. Estimate the final regression model (and data if you dropped any outliers or transformed variables) you reached in PART I using the weighted least squares (WLS) estimation. The first task would be to generate the weight variable using the approach we discussed in class. After running weighted least squares regression analysis, discuss the differences and similarities in results (e.g., model fit, regression coefficients, and standard errors) between OLS and WLS estimation.
Provide the appropriate (selected) SPSS or R output in your appendix.
Attachment:- Assignment Files.rar