Regression Project of Statistics

Anonymous
timer Asked: Nov 9th, 2016

Question description

Check the instructions (MS Word) and the excel sheet.

5-Year Return 5.0 5.3 5.0 5.4 4.8 5.9 5.0 5.6 5.0 5.1 5.6 4.7 5.1 4.8 5.2 5.4 4.9 4.7 5.2 4.7 4.9 4.7 6.1 4.2 6.3 4.5 4.6 4.3 4.7 4.4 5.6 4.6 5.0 6.2 4.6 4.2 5.2 5.2 4.5 4.6 5.7 4.2 4.6 6.5 4.7 4.0 Assets Expense Ratio 1-Year Return 3-Year Return CategoryCODE 158.2 0.61 7.6 6.3 1 420.6 0.61 8.9 6.7 1 243.1 0.93 11.1 7.4 1 24.7 0.49 7.3 6.5 1 462.2 0.62 6.9 6.0 1 497.7 0.27 11.4 7.7 1 4245.4 0.45 7.1 6.0 1 6337.8 0.45 11.0 7.4 1 1609.6 0.45 10.1 7.2 1 414.3 0.50 7.7 6.1 1 457.2 0.55 12.4 7.6 1 93.8 0.55 6.0 5.9 1 152.5 0.72 8.4 6.3 1 552.2 0.51 7.2 5.9 1 14724.5 0.21 7.2 6.2 1 217.2 0.66 10.6 7.1 1 491.6 1.06 11.6 6.9 1 1255.0 0.49 7.1 5.8 1 858.2 0.49 9.5 7.1 1 107.7 0.67 8.2 6.4 1 120.2 0.65 8.3 6.2 1 23.5 0.74 8.7 6.2 1 303.2 0.30 13.9 8.4 1 1100.4 0.23 8.4 5.9 1 1332.0 0.13 12.9 8.6 1 2205.2 0.58 5.7 5.3 1 394.6 0.67 6.9 5.7 1 286.1 0.36 3.3 4.8 1 5832.8 0.73 6.9 5.6 1 114.8 1.09 7.9 6.0 1 629.4 0.55 9.4 6.7 1 377.7 0.60 6.4 5.8 1 101.8 0.81 7.3 6.3 1 222.0 0.26 13.8 8.4 1 536.1 0.90 4.9 5.5 1 901.7 0.50 4.0 5.0 1 90.7 0.75 11.2 7.6 1 408.4 0.99 7.1 6.3 1 1327.0 0.63 5.6 5.3 1 98.0 0.60 6.3 5.7 1 661.0 0.57 14.1 8.7 1 473.1 0.77 3.4 4.8 1 91.5 0.93 8.2 6.3 1 4555.9 0.10 13.5 8.9 1 1083.4 0.96 7.6 6.0 1 205.2 1.11 6.0 5.4 1 4.2 4.0 4.7 4.5 3.7 4.7 4.1 3.9 3.9 4.2 3.7 5.0 4.2 4.5 6.4 4.6 3.5 3.4 4.9 4.2 4.7 4.9 5.4 4.6 1.8 3.8 3.3 2.9 2.2 2.0 2.3 3.3 4.0 3.0 2.7 2.9 2.8 2.2 3.6 2.6 3.1 2.8 2.1 1.1 3.5 3.4 3.2 38.7 526.4 271.1 4858.7 259.2 563.5 1850.0 598.2 354.7 246.9 14.0 122.4 523.8 539.2 135.7 199.5 170.4 306.6 865.4 148.3 31.0 254.7 221.3 517.4 54.3 773.2 590.5 411.5 101.5 462.5 1244.0 119.8 339.2 430.7 1200.7 761.7 607.7 961.7 49.1 47.4 916.2 732.5 140.5 86.2 250.1 1721.1 71.9 0.95 0.83 0.57 0.74 1.07 0.98 0.82 0.96 1.00 1.10 1.72 0.92 0.92 0.96 0.79 1.05 0.80 0.80 0.80 1.13 0.73 0.99 0.99 1.11 0.49 1.07 0.99 0.67 0.70 0.35 -0.60 1.00 1.04 0.81 0.87 0.90 1.03 0.99 1.52 1.82 1.02 0.94 0.73 1.14 0.65 0.56 0.31 6.2 3.6 6.9 7.7 5.0 8.4 4.9 3.4 4.2 6.5 5.2 10.4 4.6 6.8 15.0 9.1 0.8 0.1 8.5 7.6 7.9 8.7 11.5 8.3 -6.9 5.7 3.3 -2.0 -3.7 -3.0 -0.6 3.7 5.9 1.1 -2.5 -2.4 -1.6 -4.9 8.8 -2.3 -0.8 -1.9 -1.4 -8.6 4.6 3.6 3.9 5.3 4.5 6.0 5.8 5.1 5.8 4.8 4.5 4.8 5.2 5.7 6.7 5.1 5.6 8.3 6.3 3.9 3.5 6.4 5.7 6.2 6.4 7.0 5.8 1.2 4.3 3.9 3.0 1.8 2.7 2.6 3.8 5.2 3.1 2.2 2.6 3.3 1.9 5.7 2.4 2.9 2.6 2.0 -0.2 4.7 4.7 4.5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 3.8 3.2 3.0 3.3 3.4 2.8 3.4 3.0 3.0 3.8 3.1 2.9 2.9 3.2 2.7 2.7 2.3 3.6 3.1 2.9 3.3 3.9 3.1 3.3 3.6 3.3 2.6 2.5 1.7 2.9 2.0 1.6 1.8 3.0 2.8 2.8 2.4 2.4 2.6 2.1 2.4 2.4 2.5 3.1 2.3 2.2 1.3 36.3 175.3 33.7 132.2 261.5 144.9 1237.4 189.2 86.7 242.1 35.6 41.1 60.8 119.3 132.6 352.7 12.0 93.4 17.1 1830.6 45.7 3679.7 24.7 150.0 1044.5 252.6 732.5 162.1 549.7 44.8 56.8 100.9 203.2 171.8 299.8 6868.1 50.8 205.1 286.9 113.9 127.4 621.3 391.3 86.7 242.3 3924.1 342.5 0.60 0.45 0.77 0.53 0.38 0.45 1.08 0.25 1.00 1.12 0.60 1.24 0.85 0.36 0.71 0.52 1.02 0.53 0.80 0.55 0.74 0.18 0.75 0.71 0.48 0.84 0.67 0.54 0.54 0.88 0.39 0.59 0.80 0.55 0.50 0.46 0.98 0.51 0.46 0.96 0.65 0.69 0.65 0.97 0.87 0.67 0.62 6.5 2.8 3.7 3.6 3.0 -0.3 -1.0 0.4 1.4 7.4 0.4 2.2 1.8 3.1 0.2 1.1 1.6 4.6 3.4 1.2 3.2 5.4 2.5 2.3 -0.3 2.2 -6.9 -1.3 -2.5 2.6 -3.0 -3.3 -3.5 -3.3 -0.1 -1.3 2.6 -0.6 -1.0 -0.1 0.2 -2.6 -1.5 3.5 -0.6 -1.4 -3.8 5.7 4.2 4.4 4.6 4.5 4.5 3.3 3.5 3.7 5.5 3.6 3.8 3.7 4.3 3.3 3.7 3.3 4.9 4.3 3.7 4.3 5.6 4.4 4.1 3.2 4.1 1.3 2.5 1.5 3.9 2.1 1.4 1.8 3.4 3.5 3.4 3.9 2.8 3.4 2.8 3.1 2.6 2.5 4.3 2.7 2.5 1.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.6 0.3 0.5 0.9 2.7 0.5 1.3 1.6 1.9 2.1 0.6 2.1 1.5 2.5 3.2 1.5 1.5 0.0 2.4 1.9 1.3 1.3 1.6 2.0 2.2 1.7 0.0 -0.7 -1.9 -1.6 -0.7 -0.3 -1.6 -1.1 -1.3 -1.6 -0.1 -0.8 -2.6 -5.2 376.9 416.3 248.2 177.6 226.0 132.8 5417.5 256.7 516.0 79.1 118.5 213.8 346.4 109.7 105.1 234.7 287.2 205.1 45.1 129.2 368.3 109.7 82.8 9179.1 117.4 93.8 39.4 22.6 92.2 96.3 180.7 813.2 45.7 51.5 60.9 49.6 1070.8 65.1 397.5 64.9 0.60 0.85 1.04 0.89 0.94 0.70 0.45 0.60 0.54 1.06 1.01 0.87 0.64 0.50 0.55 0.70 0.55 1.28 0.59 0.99 0.39 1.10 0.80 0.21 0.73 0.60 0.82 0.81 0.60 1.00 0.52 0.58 0.93 0.70 0.98 0.89 0.70 0.41 0.45 0.48 -2.3 -9.4 -7.1 -5.5 0.8 -9.7 -3.7 -4.2 -2.9 0.4 -4.5 -1.1 -4.2 -2.4 2.7 -4.6 -5.4 -9.9 -2.1 -3.6 -5.9 -9.3 -9.2 -4.7 -2.2 -2.0 -10.3 -16.7 -18.9 -16.5 -12.2 -14.7 -16.0 -16.0 -16.9 -15.4 -14.0 -13.2 -21.0 -31.9 2.8 -0.3 -0.1 0.4 3.6 -0.4 0.8 1.8 2.3 3.0 0.5 2.7 1.4 3.0 4.3 1.6 1.1 -1.3 3.0 1.9 0.9 0.0 0.3 1.9 2.2 1.2 -1.4 -2.9 -4.3 -3.8 -2.3 2.4 -3.5 -2.7 -4.7 -3.4 -2.2 -2.7 -5.2 9.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Category Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Risk Average Average Above Average Above Average Average Above Average Below Average Above Average Average Average Average Below Average Average Average Average Above Average Average Below Average Above Average Average Average Average Above Average Below Average Above Average Below Average Below Average Below Average Below Average Average Above Average Below Average Average Above Average Below Average Below Average Above Average Below Average Below Average Below Average Above Average Below Average Average Above Average Average Below Average Fees No No No No No No No No No No No No No No No No Yes No No No No No No No No No No No Yes No No No No No Yes No No Yes No No No No No No No No Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Intermediate Govt Short Term Corp Short Term Corp Short Term Corp Below Average Average Above Average Above Average Below Average Above Average Average Below Average Average Below Average Above Average Above Average Average Average Above Average Above Average Below Average Below Average Average Average Below Average Above Average Average Average Above Average Above Average Above Average Average Below Average Average Below Average Average Above Average Below Average Above Average Above Average Above Average Above Average Above Average Below Average Above Average Below Average Above Average Above Average Below Average Below Average Below Average No No No Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes No No Yes Yes Yes Yes Yes Yes No Yes Yes No No No No Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes No Yes No No No Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Below Average Below Average Below Average Below Average Below Average Below Average Average Below Average Below Average Average Average Below Average Below Average Average Below Average Below Average Below Average Average Below Average Below Average Below Average Average Below Average Average Below Average Average Average Below Average Below Average Average Below Average Below Average Below Average Average Average Above Average Below Average Average Average Below Average Below Average Average Average Average Below Average Average Below Average No No No No No No Yes No Yes Yes No No No No No No No No Yes No No No No No No Yes No No No No No No No No No No Yes No No No No No No No No Yes No Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Short Term Corp Above Average Above Average Average Average Average Average Below Average Average Average Average Below Average Above Average Average Above Average Above Average Average Average Below Average Above Average Above Average Average Above Average Above Average Average Above Average Above Average Average Above Average Above Average Above Average Above Average Above Average Above Average Above Average Above Average Above Average Above Average Above Average Above Average Above Average No No Yes No Yes Yes No No No No Yes Yes Yes No No No No No No Yes No No No No No No No No No No No No No No Yes Yes Yes No No No A random sample of 180 bond funds and their characteristics Source: Berenson, Levine, Krehbiel Basic Business Statistics: Concepts and Applications (12th edition), Pearson Variables: Five-Year Return Assets (in millions billions of of dollars) dollars) Expense Ratio One-Year Return Three-Year Return Category Risk Fees Five-year return on investment in percent Percentage of assets paid paidasby a fee fundholders for management for management of the fund of the fund One-year return on investment in percent Three-year return on investment in percent 1=Intermediate Government 0=Short Term Corporate Risk of fund Above average, Average or Below average Managerial fees charged Yes or No 2th edition), Pearson Frequency Distribution for 5-Year Return bins midpts -6.01 -5.01 -4.01 -3.01 -2.01 -1.01 -0.01 0.99 1.99 2.99 3.99 4.99 5.99 6.99 Total -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 Frequency Percentage 0 0.0% 1 0.6% 0 0.0% 0 0.0% 1 0.6% 6 3.3% 5 2.8% 7 3.9% 17 9.4% 41 22.8% 37 20.6% 39 21.7% 21 11.7% 5 2.8% 180 100.0% H
To develop your project report (to be submitted for grade in hard copy) follow the steps below. 1. Create an introductory “scenario” of just two to three sentences that describes the data file for your project and why you (the ?????? Corporation/Group) are building a regression model to predict based on the set of possible independent variables 2. As you learned in class in Week 2, first develop a simple linear regression model using one of the above predictors of . 1. Cut and paste into your report the scatter plot and the Minitab Express printout for this simple linear regression model. 2. Write the sample regression equation. 3. Interpret the meaning of the intercept and slope for your fitted model. 4. Interpret the meaning of the coefficient of determination . 5. Interpret the meaning of the standard error of the estimate . 6. Obtain the residual plots and cut and paste them into the report. Briefly comment on the appropriateness of your fitted model. 1. If the assumptions are met and the fitted model is appropriate continue to Step 2G. 2. If the linearity or normality assumptions are problematic state this but continue to Step 2G with caution. You do not need to check the assumption of independence in your project – that assumption is met. 3. If the equality of variance assumption appears to be seriously violated contact me. 1. Comment on the statistical significance of your fitted model. (Note: Every team should have a fitted model that is statistically significant so contact me immediately if this is not so). 2. Select a value for your independent variable in its relevant range: 1. Predict . 2. Determine the 95% confidence interval estimate of the average value of for all occasions when the independent variable has the particular value you selected. 3. Determine the 95% prediction interval estimate of for an individual occasion when the independent variable has the particular value you selected. 1. As you learned in class in Weeks 3 and 4, you will be using the set of potentially meaningful numerical independent variables and one selected “two-category” dummy variable in your study to develop a “best” multiple regression model for predicting your numerical dependent variable . Follow the “9-step modeling process” described in the Powerpoints at the end of Module 4. 1. Start with a visual assessment of the possible relationships of your numerical dependent variable Y with each potential predictor variable by developing their respective scatter plots and paste these into your report. 2. Then fit a preliminary multiple regression model using these potential numerical predictor variables and, at most, one categorical dummy variable. 3. Then review Slides 6 through 16 of the Module 4 Powerpoints and assess collinearity until you are satisfied that you have a final set of possible predictors that are “independent,” i.e., not unduly correlated with each other. 4. Use both stepwise regression approaches and best subsets regression approaches to fit a multiple regression model with this set of potentially meaningful numerical independent variables (and, if appropriate, the one selected categorical dummy variable). 1. Based on the stepwise modeling criterion determine which numerical independent variable or variables should be included in your regression model. 2. Based on the forward selection modeling criterion determine which numerical independent variable or variables should be included in your regression model. 3. Based on the backward elimination modeling criterion determine which numerical independent variable or variables should be included in your regression model. 4. Based on the adjusted criterion determine which numerical independent variable or variables should be included in your regression model. 5. Based on Minitab’s “predicted” criterion determine which numerical independent variable or variables should be included in your regression model. 6. Based on the smallest criterion determine which numerical independent variable or variables should be included in your regression model. 7. Based on Mallows’ criterion determine which numerical independent variable or variables should be included in your regression model. 1. Comment on the consistency of your findings in Step 3D (1)-(7). 2. Cut and paste the Minitab Express printouts from Step 3D into your report. 3. Based on Step 3D (along with the principle of parsimony if necessary) select a “best” multiple regression model. 4. Using the predictor variables from your selected “best” multiple regression model, rerun the multiple regression model in order to assess its assumptions. 5. Look at the set of residual plots, cut and pasted them into the report, and briefly comment on the appropriateness of your fitted model. 1. If the assumptions are met and the fitted model is appropriate continue to Step 3J. 2. If the linearity or normality assumptions are problematic state this but continue to Step 3J with caution. You do not need to check the assumption of independence in your project – that assumption is met. 3. If the equality of variance assumption is violated either transform the dependent variable to log or transform particular independent variables (discuss this with me) and rerun the multiple regression model as in Step 3H. 1. Assess the significance of the overall fitted model. 2. Assess the contribution of each predictor variable. 1. Write the sample multiple regression equation for the “final best” model you have developed. 1. Interpret the meaning of the intercept and interpret the meaning of all the slopes for your fitted model (but do this in whatever units you used for Y to build the model). 2. Interpret the meaning of the coefficient of multiple determination . 3. Very briefly comment on how much has changed from the simple regression model in Step 2D to the “final” multiple regression model in Step 4B. 4. Interpret the meaning of the standard error of the estimate (in the units you used to build the model). 5. Select one value for each of your independent variables in their respective relevant ranges: 1. Predict . (If you used log Y take the antilog so you are back in units of Y). 2. Determine the 95% confidence interval estimate of the average value of for all occasions when the independent variables have the particular values you selected. (If your lower and upper boundaries are in units of log convert back to by taking the antilogs). 1. Determine the 95% prediction interval estimate of for an individual occasion when the independent variables have the particular values you selected. (If your lower and upper boundaries are in units of log convert back to by taking the antilogs). 1. For your “final best” model, as per Module 1, prepare a brief descriptive analysis highlighting the key measures of central tendency, variation, and shape for your dependent variable Y and for each of the predictor variables. Show the individual histograms and boxplots for these variables. If a dummy variable was included as a predictor in your “final best” model show its summary table and bar chart. Specific instructions for the written team project report follows. Writing the Team Report Each team report has a title page followed by an Introduction section describing the study “scenario” and mentioning the possible predictor variables and the dependent variable. A section on the Simple Linear Regression Model is then followed by a section on the “final best” Multiple Regression Model. The final section of the report is a Discussion section assessing the gains (if any) by using the “best” multiple regression model in lieu of the simple linear regression model. All discussed Minitab Express printouts should be “cut and pasted” into the report. These should be placed either in the body of the report or in an Appendix to the report. If the latter approach is taken, be sure to number and reference these printouts when discussing them in the body of the report. ** you should do it withe Minitab Expiress(((The INFO 561 course will be using Minitab Express, the educational version of a professional statistical software package that you can rent for $30 (for six months) at the website www.OntheHub.com Minitab Express works on all PCs and also on a Mac. Come to the first class session with Minitab Express loaded on your PC or Mac)) my project is about BOUND FUNDS STUDY the file is with attachment

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