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STAT4038/STAT6038 REGRESSION MODELLING Assignment 1 for Semester 2, 2023
发布时间：2023-08-22
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RESEARCH SCHOOL OF FINANCE, ACTUARIAL STUDIES AND STATISTICS
REGRESSION MODELLING
(STAT4038/STAT6038)
Assignment 1 for Semester 2, 2023
INSTRUCTIONS:
• This assignment is a total of 60 marks worth 15% of your overall grade for this course.
• Please submit your assignment in the Assignment section on Wattle using the Turnitin submission link. When uploading to Wattle you must submit the following, combined into a single ’PDF’ document:
1. Your assignment/report in a pdf document.
2. All your R codes you have used for the assignment added as an Appendix to the end of the report. Failure to upload the R code will result in a penalty.
• Assignment solutions should be typed. Your assignment may include some carefully edited R output (e.g. graphs, tables) showing the results of your data analysis and a discussion of these results, as well as some carefully selected code. Please be selective about what you present and only include as much R output as necessary to justify your solution. It is important to be be concise in your discussion of the results. Clearly label each part of your report with the part of the question that it refers to.
• Unless otherwise advised, use a significance level of 5%.
• Marks may be deducted if these instructions are not strictly adhered to, and marks will certainly be deducted if the total report is of an unreasonable length, i.e. more than 10 pages including graphs and tables. You must include an appendix that is in addition to the above page limits which include all the R code. Although, the appendix will not be marked but if the R codes are not provided then marks will be deducted. The R codes are required should there be any question the markers have about the work you have submitted.
• You may ask me (Abhinav Mehta) questions about this assignment up to 24 hours before the submission time. This will allow me enough time to respond to your ques- tions. The tutors will not entertain any questions about the assignment other than troubleshooting R codes.
• Late submissions are not allowed. If the assignment is not submitted by the due date then it will be redeemed for the final exam.
• Extensions will usually be granted on medical or compassionate grounds on production of appropriate evidence. You must have applied for an extension before the submission deadline for it to be considered. All extensions are to be applied via the extensions portal available on the wattle page for this course.
Question 1 [60 Marks]
We have the end of day values for the index bond but in order to use the index in financial applications it would be preferred to have access to intraday values rather than end of day values. We want to predict intraday movement of a bond index using price of Exchange Traded Funds (ETFs). To this extent we can use information on ETFs to predict the bond values. The . csv file ‘etf’ contains a year’s worth of data on the end of day values on the index bond, H0A0 as well as the daily price on one of the ETFs, JNK.
(a) [10 marks] Conduct an exploratory data analysis to assess whether the two vari- ables are associated. Is there a statistically significant correlation between the vari- ables? Use the cor. test() function to conduct a suitable hypothesis test. Clearly specify the hypotheses you are testing and present and interpret the results.
(b) [20 marks] Fit a simple linear regression (SLR) model with H0A0 as the response variable and JNK as the predictor. Construct a plot of the residuals against the fitted values, a normal Q-Q plot of the residuals, a bar plot of the leverages for each observation and a bar plot of Cook’s distances for each observation. Use these plots (and other means) to comment on the model assumptions and on any unusual data points.
(c) [5 marks] If there are any violations of the assumptions of regression model then briefly comment on how you would resolve these issues.
(d) [10 marks] What are the estimated coefficients of the SLR model in part (b) and the standard errors associated with these coefficients? Interpret the values of these estimated coefficients and perform t-tests to test whether or not these coefficients differ significantly from zero. What do you conclude as a result of these t-tests?
(e) [10 marks] Produce the ANOVA (Analysis of Variance) table for the SLR model and interpret the results of the F-test. What is the coefficient of determination for this model and how should you interpret this summary measure?
(f) [5 marks] The JNK value on a particular day was 37.55. What is the expected value for H0A0 on that day? Construct an appropriate 99% interval estimate for this value of the bond index.
