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Assume thаt yоu purchаse а 10-year bоnd. This bоnd pays an annual coupon of $40 each year and has a maturity value of $1,000. When you bought this bond, you required a 10 percent rate of return (you should now be able to determine how much you paid for this bond). Assume that right after you bought this bond, interest rates dropped to 8 percent and remained at that rate. If you only hold this bond for 5 years and then sell it in the market, determine your realized compounded yield. (Hint: at what rate is interest income reinvested?)
Q1. Dаtа Explоrаtiоn (Use dataset cоmpleted_course for this question) (13 points) (4 points) a) Create a visualization to compare the distribution of Hours_Studied across different Enrollment_Types (Free vs. Paid) and Completion statuses (Completed vs. Not Completed). Discuss any observable trends or patterns. (3 points) b) Compute correlation matrix for numerical variables grouped by Completed. Explain the results. (2 points) c) Which Region has the highest completion rate? (4 points) d) What is the proportion of students who completed the course for each Gender?Use barplots to show the distribution of students by Gender and region?
Q2 Lоgistic Regressiоn mоdel (Use trаinDаtа for this question) (30 points) ( 5 points) a) Create a logistic regression model using Completed as the response variable and the following predicitng variables: Hours_Studied, Age, Region. Call it *model1*. Display the summary. Using "model1", interpret the coefficients of the following predictors below with respect to BOTH the log-odds of turnover and the odds of completed. 1) Hours_Studied 2) RegionWest (5 points) b) Using the "trainData" dataset, create a logistic regression model using Completed as response variable and all variables in "trainData" as predictors (call it model2) and display the summary of model2. Using the model coefficients, how would you compute the predicted probability of completion for a 30-year-old male from the South enrolled in the free course who studied 10 hours and submitted 5 assignments? (10 points) c) This dataset is without replications. Aggregate the response data to convert it into binary data with replications. (Use categorical variables only)Fit the following logistic models:i) Using aggregated data. Call it model.agg. Display the summaryii) Using the non-aggregated data. Call it model.withoutagg. Display the summary. (Use the same categorical variables as in model.agg) What is the difference between the coefficients of both the models? ExplainHow are the null and residual deviance different for both models? Explain (3 points) d) Perform a test for overall regression of the logistic regression "model.agg", using a significance level of alpha=0.05. Does the overall regression have explanatory power? Provide interpretation of the test. (3 points) e) Perform the goodness of fit test on model.agg using deviance and Pearson residuals and interpret the results. (4 points) f) Evaluate the predicting power of the "model.withoutagg" in Q2c using cross validation.