1. The dataset, acath.csv, contains real-world data regarding cardiac catheterization procedures. If you are unfamiliar with this procedure, it is used to diagnose and treat heart problems. A long, thin tube is inserted into an artery in your groin, neck, or arm and threaded to your heart. Variables in the dataset are defined below. Name Gender Age Duration Cholest Sigdz Tvdlm Labels Gender, {0=female, 1=male} Age, {0, 1, 2,..} Duration of Symptoms of Coronary Artery Disease in months Cholesterol in mg/dl Significant Coronary Disease by Cardiac Cath coded {0=not significant, 1=significant} Three Vessel or Left Main Disease by Cardiac Cath, {0=absent, 1=present} a. State the levels of measurement for all variables. Justify. > data1<-read.csv(file.choose(),header=T) > data1 gender age duration chol sigdz tvdlm 1 0 17 1 120 0 0 2 0 18 0 NA 0 0 3 0 19 1 150 0 0 4 0 20 7 170 0 0 5 1 20 11 178 0 0 6 1 22 4 188 0 0 7 0 22 7 NA 0 0 8 0 23 6 251 0 0 9 0 24 31 190 0 0 10 0 24 41 157 0 0 11 1 25 4 188 1 1 12 1 25 6 310 1 0 13 0 25 2 202 0 0 14 1 25 2 153 0 0 15 0 26 2 230 0 0 16 1 26 3 186 0 0 17 0 27 1 NA 0 0 18 0 27 6 192 0 0 19 0 27 8 230 0 0 20 1 27 1 172 0 0 .... > names(data1) [1] "gender" "age" > levels("gender") NULL > levels("age") NULL > levels("duration") NULL > levels("chol") NULL > levels ("sigdz") NULL > levels ("tvdlm") NULL "duration" "chol" "sigdz" "tvdlm" Nominal measurements- data in the form of names, categories, or labels Interval Level of Measurement: temperature in degrees Quantitative measurements: data in numerical form Qualitative measurements: categorical data that doesn't include numbers References: Statistics Solutions. 2015. https://www.statisticssolutions.com/data-levels-ofmeasurement/ Lane, D. M., & Osherson, D. (2013). Levels of Measurement. In D. M. Lane, Introduction to Statistics (pp. 34-39). Houston. b. Provide descriptive statistics as well as appropriate graphs for both age and tvdlm. Interpret. Provide side-by-side boxplots for tvdlm and age. Interpret. c. Test the hypotheses that gender and the presence of significant disease are independent. Use alpha =.01. Provide a 99% confidence interval. What are the implications of your results? d. Build a 99% confidence interval for age. Test whether the mean age is 51.84 years using alpha =.01. e. Test whether log(duration+.5) is a function of age. Provide separate boxplots for duration as well as log(duration+.5). (Do not do side-by-side.) Explain why the log was used and + .5 was added. Plot the relationship. Fit a line for the relationship. Provide and interpret the ANOVA table. Interpret the R 2 and standard error. Forecast log(duration+.5) for age = 80, and convert back to the untransformed variable, age. Forecast log(duration+.5) for age = 10. 2. This problem requires the use of the Challenger dataset.If you recall, the variables in the data set are defined as follows: launch: this numbers the temperature-sorted observations from 1 to 23. temp: temperature in degrees Fahrenheit at the time of launch incident: If there was an incident with an O-Ring, then it is coded "Yes." o_ring_probs: counts the number of O-ring partial failures experienced on the flight. a. In the already temperature-sorted dataset, find on which observation the first successful launch occurred (one with no incident).________Test the hypothesis that the first failure would come on or after this observation. Use alpha = .10. b. How many failures occurred above 65 degrees F? _____ Test the hypothesis that you would see this many or fewer failures given a fixed population of 23 launches. c. What was the overall failure probability? _____How many failures occurred below 65 degrees F? _____ Assume that the launches represent a sequential sample (independent events). Test the hypothesis that you would see this many failures or more. d. How many o-ring problems (not incidents, o_ring_probs) occurred in the 23 launches? _____How many of these failures occurred in the first four temperature sorted launches? _____ Test the hypothesis of obtaining that amount or a more extreme amount of failures if the failure rate was constant. e. Provide a 90% confidence interval for incidents. 3. The accumrates.csv data set contains information on various funds as discussed in class. The TSP is a retirement contribution plan for federal civilians and uniformed military personnel of the United States, similar to a traditional 401K plan. Participants are offered five different funds including the Government Security Fund (or G Fund), the Fixed Income Index Investment Fund (or F Fund), the Common Stock Index Fund (or C Fund), the Small Capitalization Stock Index Fund (or S Fund), and the International Stock Index Investment Fund (or I Fund). The G Fund is invested in short-term government securities issued by the Treasury and investment risk is near zero. The F Fund objective is to match the Barclay's Capital U.S. Aggregate Index, which provides a broad representation of the U.S. bond market. The C Fund objective is to track the Standard and Poor's 500 (S&P 500), which provides representation for medium and large capitalization stocks. The S Fund objective is to match the Dow Jones U.S. Completion Total Stock Market Index. Finally, the I Fund attempts to match the performance of the Morgan Stanley Capital International EAFE (Europe, Australasia, Far East) Index (Thrift Savings Plan, 2014). a. Provide appropriate descriptive statistics / graphs for the CFund accumulation rates. If you invested $100,000 in the CFund at the beginning of January 2003, what would it have been worth at the end of December, 2014? What would this same $100,000 be worth if you invested it all in the SFund? The IFund? b. The Coefficient of Variation (CV) is a measure of risk. It is defined as the (standard deviation / mean) x 100 %. The higher the coefficient of variation, the higher the risk associated with an investment. Calculate the CVs for all funds. Which fund is the riskiest? Which fund is least risky? Does this make sense based on the investment strategies? c. Test the hypothesis that the CFund accumulation rates are related to the month. Use alpha = .10 d. Test the hypothesis that the CFund accumulation rates are related to the year. Be sure to make year a factor (i.e., factor(Year)), so that you can see any non-constant effects Use alpha = .10 e. Plot the relationship between the CFund and the SFund. Next, plot the relationship between the CFund at time t and the SFund at time t-1. What is the implication? Run a regression of both relationships (CFund vs. SFund, and CFund(t) vs. SFund(t-1). Interpret the results. Are you surprised? f. Provide a 99% confidence interval for the GFund. Test whether this is truly a no risk fund (e.g., accumulation rates greater than 1) at that level. gender age duration chol sigdz tvdlm 0 17 1 120 0 0 0 18 0 0 0 0 19 1 150 0 0 0 20 7 170 0 0 1 20 11 178 0 0 1 22 4 188 0 0 0 22 7 0 0 0 23 6 251 0 0 0 24 31 190 0 0 0 24 41 157 0 0 1 25 4 188 1 1 1 25 6 310 1 0 0 25 2 202 0 0 1 25 2 153 0 0 0 26 2 230 0 0 1 26 3 186 0 0 0 27 1 0 0 0 27 6 192 0 0 0 27 8 230 0 0 1 27 1 172 0 0 0 27 0 0 0 0 28 0 173 0 0 1 28 9 199 0 0 1 28 3 108 0 0 0 28 1 212 0 0 0 28 11 234 0 0 0 28 13 375 1 1 0 28 2 166 0 0 0 28 57 0 0 0 28 15 229 0 0 0 28 63 0 0 0 28 0 0 0 1 29 18 215 0 0 1 29 8 268 1 1 1 29 5 174 0 0 0 29 3 270 0 0 0 29 4 187 0 0 0 29 7 317 1 0 1 29 6 185 0 0 0 29 13 1 0 0 29 0 0 0 0 30 15 165 0 0 0 30 9 250 1 1 0 30 2 185 0 0 0 30 17 220 0 0 1 30 6 350 0 0 1 30 17 230 0 0 0 30 3 146 1 0 1 30 2 325 0 0 0 30 2 1 0 0 30 1 0 0 0 31 0 299 1 0 1 31 13 198 1 0 0 31 1 302 1 0 0 31 36 232 0 0 1 31 10 204 0 0 0 31 11 219 0 0 0 31 14 170 0 0 1 31 24 155 0 0 0 31 2 225 1 0 1 31 174 210 0 0 0 31 3 180 0 0 0 31 1 185 0 0 0 31 19 197 0 0 0 31 30 253 0 0 0 31 0 1 0 0 31 13 204 0 0 0 31 73 0 0 0 31 16 0 0 1 32 42 174 0 0 1 32 3 0 0 0 32 10 170 0 0 0 32 10 227 0 0 0 32 1 205 0 0 1 32 33 244 0 0 0 32 29 175 1 0 0 32 0 0 0 0 32 8 150 0 0 0 32 8 235 1 1 0 32 0 187 1 0 0 32 10 1 0 1 32 62 159 0 0 0 32 6 269 0 0 0 32 1 175 1 0 1 32 23 0 0 0 32 77 0 0 0 33 5 241 1 0 0 33 1 148 1 0 0 33 2 272 1 0 1 33 18 270 1 0 0 33 10 230 0 0 0 33 60 294 0 0 0 33 5 262 0 0 1 33 20 140 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 33 33 33 33 33 33 33 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 6 5 54 11 1 6 16 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1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 Year Month GFund FFund CFund SFund IFund TimePeriod 2003 Jan 1.0035 1.001 0.9733 0.9765 0.9576 1 2003 Feb 1.0032 1.0141 0.9851 0.9744 0.9771 2 2003 Mar 1.0033 0.9995 1.0097 1.0155 0.981 3 2003 Apr 1.0033 1.0083 1.0826 1.0831 1.0982 4 2003 May 1.0034 1.0187 1.0526 1.0942 1.0607 5 2003 Jun 1.002 0.997 1.012 1.022 1.023 6 2003 Jul 1.003 0.9749 1.0148 1.0421 1.0254 7 2003 Aug 1.004 0.9979 1.0224 1.0451 1.0219 8 2003 Sep 1.004 1.0268 0.9886 0.9865 1.0308 9 2003 Oct 1.003 0.99 1.0568 1.0765 1.0606 10 2003 Nov 1.003 1.003 1.0091 1.0347 1.0222 11 2003 Dec 1.0049 1.0101 1.0524 1.0204 1.0768 12 2004 Jan 1.0029 1.008 1.018 1.0353 1.0132 13 2004 Feb 1.0039 1.0109 1.0135 1.0178 1.0222 14 2004 Mar 1.0029 1.0069 0.985 1.0038 1.006 15 2004 Apr 1.0029 0.9746 0.9848 0.9606 0.9769 16 2004 May 1.0039 0.995 1.0137 1.015 1.003 17 2004 Jun 1.0038 1.006 1.0186 1.0272 1.0289 18 2004 Jul 1.0038 1.01 0.9676 0.9448 0.9624 19 2004 Aug 1.0038 1.0188 1.0034 1 1.01 20 2004 Sep 1.0038 1.0029 1.0111 1.0392 1.0205 21 2004 Oct 1.0038 1.0087 1.0152 1.0185 1.0394 22 2004 Nov 1.0028 0.9914 1.0408 1.0696 1.0616 23 2004 Dec 1.0038 1.0097 1.0336 1.0417 1.0438 24 2005 Jan 1.0037 1.0058 0.976 0.9661 0.9813 25 2005 Feb 1.0037 0.9943 1.0206 1.0204 1.0434 26 2005 Mar 1.0037 0.9952 0.9829 0.9814 0.9748 27 2005 Apr 1.0037 1.0135 0.981 0.9628 0.9773 28 2005 May 1.0037 1.0105 1.0315 1.0605 0.996 29 2005 Jun 1.0028 1.0056 1.0016 1.0337 1.0186 30 2005 Jul 1.0037 0.9916 1.0367 1.0559 1.0307 31 2005 Aug 1.0037 1.0123 0.991 0.9899 1.0323 32 2005 Sep 1.0036 0.9897 1.0084 1.0083 1.0368 33 2005 Oct 1.0036 0.9925 0.9834 0.9767 0.971 34 2005 Nov 1.0036 1.0038 1.0375 1.0472 1.0244 35 2005 Dec 1.0045 1.0095 1.0007 1.0037 1.0464 36 2006 Jan 1.0036 1.0009 1.0266 1.067 1.0614 37 2006 Feb 1.0036 1.0028 1.0022 0.9902 0.9973 38 2006 Mar 1.0036 0.9907 1.0129 1.0384 1.0333 39 2006 Apr 1.0044 0.9981 1.0135 1.0034 1.0483 40 2006 May 1.0044 0.9991 0.9713 0.9564 0.9613 41 2006 Jun 1.0044 1.0019 1.0007 1.0047 1 42 2006 Jul 1.0044 1.0132 1.0065 0.9721 1.0098 43 2006 Aug 1.0044 1.0158 1.0236 1.0215 1.0276 44 2006 Sep 1.0035 1.0082 1.0258 1.0088 1.0015 45 2006 Oct 1.0043 1.0073 1.0327 1.0499 1.0387 46 2006 Nov 1.0043 1.0108 1.0191 1.0354 1.0296 47 2006 Dec 1.0034 0.9946 1.0142 1.0011 1.0311 48 2007 Jan 1.0043 1 1.0153 1.0314 1.0131 49 2007 Feb 1.0034 1.0153 0.9805 0.9974 1.0018 50 2007 Mar 1.0042 1 1.0109 1.0109 1.0257 51 2007 Apr 1.0042 1.0053 1.0443 1.0251 1.0376 52 2007 May 1.0034 0.993 1.0352 1.044 1.0254 53 2007 Jun 1.0042 0.9973 0.983 0.9847 1.002 54 2007 Jul 1.005 1.008 0.969 0.9543 0.9761 55 2007 Aug 1.0033 1.0123 1.0154 1.0138 0.9929 56 2007 Sep 1.0041 1.0078 1.0376 1.0297 1.0536 57 2007 Oct 1.0041 1.0086 1.0158 1.0283 1.0449 58 2007 Nov 1.0033 1.0188 0.958 0.9435 0.9628 59 2007 Dec 1.0041 1.0025 0.9934 0.996 0.9775 60 2008 Jan 1.0033 1.0176 0.9402 0.9373 0.9148 61 2008 Feb 1.0024 1.0016 0.9672 0.9795 0.9934 62 2008 Mar 1.0032 1.0033 0.9954 0.9857 1.0018 63 2008 Apr 1.0024 0.9984 1.0494 1.053 1.0555 64 2008 May 1.0032 0.9926 1.0127 1.0488 1.0109 65 2008 Jun 1.0032 0.9992 0.9159 0.9237 0.9185 66 2008 Jul 1.004 0.9999 0.992 0.9921 0.9628 67 2008 Aug 1.0033 1.0092 1.0146 1.0217 0.9584 68 2008 Sep 1.0031 0.9869 0.9106 0.8968 0.8769 69 2008 Oct 1.0031 0.976 0.8317 0.7901 0.7941 70 2008 Nov 1.0031 1.033 0.9282 0.8887 0.9328 71 2008 Dec 1.0024 1.0373 1.0107 1.0468 1.0766 72 2009 Jan 1.0019 0.9914 0.9159 0.9181 0.8807 73 2009 Feb 1.0021 0.9961 0.8936 0.8978 0.8977 74 2009 Mar 1.0024 1.0138 1.0881 1.0864 1.072 75 2009 Apr 1.0021 1.0049 1.0958 1.15 1.1213 76 2009 May 1.0025 1.0078 1.056 1.0397 1.1341 77 2009 Jun 1.0027 1.0054 1.0024 1.0073 0.9892 78 2009 Jul 1.0028 1.0159 1.0758 1.0866 1.0974 79 2009 Aug 1.0028 1.0103 1.0362 1.0385 1.0487 80 2009 Sep 1.0026 1.0107 1.0374 1.0594 1.0379 81 2009 Oct 1.0026 1.0051 0.9814 0.9449 0.9759 82 2009 Nov 1.0026 1.013 1.06 1.0385 1.0316 83 2009 Dec 1.0025 0.9845 1.0194 1.0657 1.0143 84 2010 Jan 1.0029 1.0154 0.964 0.9757 0.9483 85 2010 Feb 1.0024 1.0038 1.0311 1.0489 1.0006 86 2010 Mar 1.0027 0.9989 1.0604 1.0739 1.0628 87 2010 Apr 1.0028 1.0107 1.0158 1.0482 0.9765 88 2010 May 1.0028 1.0085 0.9201 0.9249 0.888 89 2010 Jun 1.0024 1.0156 0.9476 0.931 0.9825 90 2010 Jul 1.0023 1.0107 1.0701 1.07 1.1078 91 2010 Aug 1.0022 1.0128 0.9549 0.9441 0.9686 92 2010 Sep 1.0017 1.0017 1.0892 1.1147 1.0981 93 2010 Oct 1.0018 1.0036 1.038 1.0448 1.0363 94 2010 Nov 2010 Dec 2011 Jan 2011 Feb 2011 Mar 2011 Apr 2011 May 2011 Jun 2011 Jul 2011 Aug 2011 Sep 2011 Oct 2011 Nov 2011 Dec 2012 Jan 2012 Feb 2012 Mar 2012 Apr 2012 May 2012 Jun 2012 Jul 2012 Aug 2012 Sep 2012 Oct 2012 Nov 2012 Dec 2013 Jan 2013 Feb 2013 Mar 2013 Apr 2013 May 2013 Jun 2013 Jul 2013 Aug 2013 Sep 2013 Oct 2013 Nov 2013 Dec 2014 Jan 2014 Feb 2014 Mar 2014 Apr 2014 May 2014 Jun 2014 Jul 2014 Aug 2014 Sep 2014 Oct 2014 Nov 2014 Dec 1.0017 1.002 1.0024 1.0022 1.0026 1.0025 1.0025 1.0021 1.0022 1.0019 1.0016 1.0014 1.0014 1.0015 1.0013 1.0012 1.0014 1.0015 1.0014 1.0011 1.0012 1.0011 1.001 1.0012 1.0011 1.0012 1.0013 1.0013 1.0013 1.0012 1.0012 1.0014 1.0018 1.0018 1.0019 1.0019 1.0018 1.0019 1.0021 1.0018 1.0019 1.002 1.002 1.0019 1.0019 1.002 1.0018 1.002 1.0017 1.0018 0.9943 0.9895 1.0013 1.0026 1.0006 1.0128 1.0131 0.997 1.0159 1.0145 1.0073 1.0011 1.0001 1.0101 1.0088 1.0005 0.9939 1.0112 1.0091 1.0005 1.0138 1.0007 1.0015 1.002 1.0016 0.9987 0.9944 1.0051 1.0007 1.0102 0.9822 0.9847 1.0013 0.9952 1.0099 1.0089 0.9965 0.9944 1.0158 1.0062 0.9985 1.009 1.0121 1.0014 0.9981 1.0112 0.9942 1.0096 1.0074 1.0021 1.0001 1.0668 1.0237 1.0342 1.0004 1.0296 0.9887 0.9833 0.9796 0.9456 0.9297 1.1093 0.9979 1.0104 1.045 1.0434 1.033 0.9938 0.9401 1.0413 1.014 1.0225 1.0257 0.9814 1.0057 1.0091 1.0518 1.0136 1.0375 1.0193 1.0234 0.9866 1.051 0.9711 1.0314 1.046 1.0305 1.0254 0.9655 1.0458 1.0085 1.0075 1.0235 1.0207 0.9863 1.0401 0.986 1.0245 1.027 0.9976 1.03 1.0738 1.0123 1.0452 1.0206 1.0294 0.9873 0.9765 0.9686 0.9188 0.8927 1.1409 0.9949 0.9996 1.0759 1.0399 1.023 0.9929 0.9309 1.0325 0.9938 1.0357 1.0251 0.9869 1.0153 1.0269 1.0696 1.01 1.0469 1.0065 1.0271 0.9901 1.0688 0.9724 1.0589 1.0294 1.0249 1.0294 0.9809 1.0543 0.9931 0.9753 1.0152 1.0445 0.9562 1.0498 0.949 1.0411 1.0133 1.0099 0.9516 1.0812 1.0241 1.0333 0.9777 1.0603 0.971 0.9884 0.984 0.9097 0.8945 1.0948 0.9754 0.9797 1.0536 1.0514 1.0013 0.9813 0.886 1.0708 1.0056 1.0329 1.0296 1.0085 1.0241 1.0402 1.0445 0.9901 1.0088 1.0532 0.9688 0.9723 1.0529 0.9869 1.0741 1.0338 1.0075 1.0151 0.9597 1.0558 0.9943 1.0151 1.0172 1.0099 0.9805 0.9986 0.9618 0.9937 1.0051 0.9587 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 4312ccc8c61f60b2c1d6a7bb519beb15a28547bb launch temp incident o_ring_probs 1 53.6 Yes 3 2 57.2 Yes 1 3 57.2 Yes 1 4 62.6 Yes 1 5 66.2 No 0 6 66.2 No 0 7 66.2 No 0 8 66.2 No 0 9 66.2 No 0 10 68 No 0 11 69.8 Yes 1 12 69.8 No 0 13 69.8 Yes 1 14 69.8 No 0 15 69.8 No 0 16 71.6 No 0 17 73.4 No 0 18 75.2 Yes 2 19 75.2 No 0 20 75.2 No 0 21 78.8 No 0 22 78.8 No 0 23 80.6 No 0 Page 1