EPE/EDP 660 Exam 3 - University of Kentucky



{2 points} Name You MUST work alone – no tutors; no help from classmates. Email me or see me with questions. You will receive a score of 0 if this rule is violated. Minitab (or other approved software) output, session window in Minitab, must be included {2 points}. Answers must be clearly labeled. If using Minitab, the session window should be included. Do NOT include a copy of the worksheet. In order to receive partial credit, work must be shown.PART A (18 POINTS): FILL IN THE BLANK (with best choice) {2 points per blank}The number of levels of a quantitative variable must be at least ______ more than the order of the polynomial x that you want to fit.When 2 or more independent variables are moderately to highly correlated with each other, it is reasonable to suspect an issue with ___________________.___________________ is predicting y when the x values are outside the range of experimentation.___________________ regression is a screening method that starts with no predictors. Each of the available predictors is evaluated with respect to how much R2 would be increased by adding it to the model.The ___________________can be regarded as a random sample from a N(0,σ2) distribution, so we can check this assumption by checking whether the residuals might have come from a normal distribution.To fit a straight line, you need at least______ different x values, and to fit a curve you need at least ______ .An observation that is larger than 2 or 3s is a/n ___________________. In ___________________ regression, the β parameter is interpreted as the percentage change in odds for every 1-unit increase in xi holding all other x’s fixed.PART B: Short Answer (23 POINTS)In addition to independent or predictor variables being highly correlated, how can you assess if multicollinearity is present? Explain. {4 points}Considering the regression setting, list the assumptions about ε? If assumptions do not hold, what are the potential consequences? Explain. {6 points)Why would we want to use the standardized β coefficients over the regular β coefficients? Explain. {4 points}What is meant by Parsimony in regards to regression models? Are there times when it is good and bad? Explain. {3 points}What is the difference between homoscedastic and heteroscedastic and which is preferable when dealing with regression modeling? {3 points}How is logistic regression unique in terms of the dependent variable? In what way/s is this helpful? {3 points}PART C: Data Analysis (55 points)A college dean desires to estimate students’ GPA after their first semester. The dean takes a random sample of 94 freshmen currently enrolled at the college and records their ACT scores, listed by section and as a comprehensive score (ACT Composite), and High School GPA (HS GPA). The table below contains data for the sample (Only the first 6 observations are presented. Use the full data set for your analysis). *Adequate ACT (highlighted in table) is discussed and used in item (i).Term GPAHS GPAACT EnglishACT MathACT ReadingACT ScienceACT CompositeAdequate ACT4.003.93252424242411.833.37232121242213.793.92291831222513.444.00283026262814.004.00272530232613.313.1916181816170Produce a graphical summary for the y-variable, Term GPA. Describe the general distribution of y, include discussion of central tendency and variability. {2 points}Produce descriptive statistics for all potential predictor (independent variables). HS GPA-ACT Comp, exclude Adequate ACT (for now). At a minimum, include mean, median, standard deviation, and range. Describe general trends, distributions, etc. {3 points}Produce a correlation matrix and matrix plot of all the variables above, excluding Adequate ACT. Do you see any “strong” correlations? Defend. {3 points}Compute the regression equation, R-square, VIF, standardized coefficient estimates, and standardized residuals, for the regression model with all potential independent variables as predictors of Term GPA, excluding Adequate ACT. (Include the ANOVA table). Submit your 1st 8 rows of the Minitab worksheet for this item. {5 points}What is the R-square and R-square (adjusted)? What does this tell us? {3 points}Overall, do you feel this is a reasonable model? Defend. {3 points}Conduct a Stepwise regression analysis of the data, excluding Adequate ACT. List the best equation. (Be sure to explain how the decision was made.) Defend. {5 points}Conduct a Backward Elimination regression analysis of the data, excluding Adequate ACT. (Be sure to explain how the decision was made.) Defend. {5 points}Conduct a Best Subsets regression analysis, include PRESS, of the data. Discuss the results. Be sure to explain what PRESS is. {3 points}Now, compute the regression equation for estimating Term GPA as a function of ACT comp and HS GPA. Include VIF, standardized coefficient estimates, and standardized residuals, along with the ANOVA table. {3 points}Check the Assumptions of Regression. Be sure that you have produced the standardized residuals 4 in 1 plot, or constructed the appropriate plots. {4 points}Produce Hi(leverages), Cook’s Distance, and DFITS. Explore, identify, and discuss outliers and leverage points. {4 points}A new variable was computed in C8, Adequate ACT. If ACT Comp score is greater than 20 then Acceptable = 1, if not then Acceptable = 0. Produce a binary logistic regression model to predict an Adequate ACT score as a function of High School GPA {2 points}.Report the maximum likelihood values of the estimates. {2 points}Report the odds-ratios and compute the percent increase or decrease in the estimate of odds of Adequate ACT. {2 points}Test the overall adequacy of the model. Be sure to report the test statistic and p-value. {3 points}From all the regression equations produced above, which do you feel is most desirable? Write the equation. Defend your choice. {3 points} ................
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