How to use an exploratory data analysis to assess whether the two variables are associated?
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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 variables are associated. Is there a statistically significant correlation between the variables? 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. Date H0A0 JNK 9/2/2014 1081.96 39.12966 9/3/2014 1081.09 39.015798 9/4/2014 1079.53 38.882963 9/5/2014 1077.24 38.845009 9/8/2014 1077.51 38.807059 9/9/2014 1075.87 38.617292 9/10/2014 1072.47 38.598315 9/11/2014 1071.06 38.560361 9/12/2014 1070.41 38.531898 9/15/14 1069.98 38.474967 9/16/14 1068.85 38.493944 9/17/14 1069.98 38.560361 9/18/14 1071.