HW 6 Answers
13 Pages

HW 6 Answers

Course Number: ECON 1001, Spring 2012

College/University: CUNY Baruch

Word Count: 5450

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AGE Module 6 Spreadsheet Assignment First, save this spreadsheet to your computer files, adding your name to the filename (e.g. SmithM6Assign.xls). Save in .xls format. Open the file on your computer, work on the problems, re-saving your file in .xls format always You may copy the data and/or problems to additional sheets in this workbook or work on this page. To add a sheet, click Shift+F11. Or right-click on the...

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6 Spreadsheet AGE Module Assignment First, save this spreadsheet to your computer files, adding your name to the filename (e.g. SmithM6Assign.xls). Save in .xls format. Open the file on your computer, work on the problems, re-saving your file in .xls format always You may copy the data and/or problems to additional sheets in this workbook or work on this page. To add a sheet, click Shift+F11. Or right-click on the sheet tab, which also allows you to rename the tab. Attach the file in the assignment drop box for Module 6. For this Problem, we will use the Bears data set provided in the Appendix B data on the CD or online -- click Tools for Success. Copy the data set into this spreadsheet. Please organize your work so that it is easily understood. Some people put each problem on a separate sheet with labelled tabs. Be sure to show your calculations and/or paste in results from StatCrunch, DDXL, etc. Remember to use 4-Step problem solving process: Declare, Strategize, Execute, Deduce. Always characterize the distributions. Problem 1 (25 points) Find the correlations of various pairs of data column: HeadLength, HeadWidth, Neck, Length, Chest, Weight (there will be 15 pairs) Show and discuss a scatterplot with regression for the best-correlated pair, and one for the least-correlated pair. HdLngth HdLngth HdWidth Neck Length Chest Weight HdWidth Neck Length Chest Weight 1 1 << fill in yellow cells 1 1 1 1 Problem 2 (25 points) It is easier to measure Head Length and Head Width than anything else. Using Head Length as the Explanatory variable, give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 12.95 for Head Length, predict each response variable. Which are you most / least confident about? Note: the regression equation is a linear equation of the form: y = m*x + b, where m is the slope and b is the y-intercept m and b are coefficients, and x and y are variables. Linear regression fits a line to the points, and determines the coefficients. Using the Excel regression tool in the Analysis Toolpak, the coefficients are given in the bottom table. StatCrunch regression provides the coefficients as intercept and slope Statdisk correlation and regression calls the coefficients y-intercept and slope DDXL simple regression refers to the y-intercept as the Constant coefficient y x value is 12.95 and you must calculate the predicted response variable y, for each of the 4 cases x 0 m Problem 3 (25 points) Similar to problem 2, use Head Width as the Explanatory variable, and give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 6.19 for Head Width, predict each response variable. Which are you most / least confident about? y This is similar to problem 2, except x value is 6.19 enter coeff's m and b x 0 result Problem 4 (25 points) Since 12.95 is average Head Length, and 6.19 is average Head Width, comment on the calculated responses in problems 2 and 3, and compare these responses with the average values of the data columns Neck, Length, Chest, Weight. (perhaps a table?) Could scientists use the Head Length and Head Width and a database of previous data to make reasonable predictions about other data for the bear population? Explain your point of view. Neck average calc-P2 calc-P3 Length Chest b 12.95 result Weight << enter averages from the respective data columns in Bears Data << enter calculated values from problem 2 << enter calculated values from problem 3 m b 6.19 enter coeff's m and b MONTH 19 55 81 115 104 100 56 51 57 53 68 8 44 32 20 32 45 9 21 177 57 81 21 9 45 9 33 57 45 21 10 82 70 10 10 34 34 34 58 58 11 23 70 11 83 35 16 16 17 17 17 8 83 18 SEX 7 7 9 7 8 4 7 4 9 5 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 11 11 10 11 11 11 4 4 5 5 5 8 11 6 HEADLEN HEADWTH 1 1 1 1 2 2 1 1 2 2 1 1 2 1 2 1 1 2 1 1 2 2 1 1 1 1 1 2 2 1 1 2 2 1 1 1 1 1 2 1 1 1 1 2 2 1 1 1 1 2 2 2 1 1 11 16.5 15.5 17 15.5 13 15 13.5 13.5 12.5 16 9 12.5 14 11.5 13 13.5 9 13 16 12.5 13 13 10 16 10 13.5 13 13 14.5 9.5 13.5 14.5 11 11.5 13 16.5 14 13.5 15.5 11.5 12 15.5 9 14.5 13.5 10 10 11.5 11.5 11 10 15.5 12.5 5.5 9 8 10 6.5 7 7.5 8 7 6 9 4.5 4.5 5 5 8 7 4.5 6 9.5 5 5 5 4 6 4 6 5.5 6.5 5.5 4.5 6.5 6.5 5 5 7 6.5 5.5 6.5 7 6 6.5 7 5 7 8.5 4 5 5 5 4.5 4.5 8 8.5 NECK LENGTH 16 28 31 31.5 22 21 26.5 27 20 18 29 13 10.5 21.5 17.5 21.5 24 12 19 30 19 20 17 13 24 13.5 22 17.5 21 20 16 28 26 17 17 21 27 24 21.5 28 16.5 19 28 15 23 23 15.5 15 17 15 13 10 30.5 18 53 67.5 72 72 62 70 73.5 68.5 64 58 73 37 63 67 52 59 64 36 59 72 57.5 61 54 40 63 43 66.5 60.5 60 61 40 64 65 49 47 59 72 65 63 70.5 48 50 76.5 46 61.5 63.5 48 41 53 52.5 46 43.5 75 57.3 CHEST 26 45 54 49 35 41 41 49 38 31 44 19 32 37 29 33 39 19 30 48 32 33 28 23 42 23 34 31 34.5 34 26 48 48 29 29.5 35 44.5 39 40 50 31 38 55 27 44 44 26 26 30.5 28 23 24 54 32.8 WEIGHT 80 344 416 348 166 220 262 360 204 144 332 34 140 180 105 166 204 26 120 436 125 132 90 40 220 46 154 116 182 150 65 356 316 94 86 150 270 202 202 365 79 148 446 62 236 212 60 64 114 76 48 29 514 140 HEADLEN Problem 1 (25 points) Find the correlations of various pairs of data column: HeadLength, HeadWidth, Neck, Length, Chest, Weight (there will be 15 pairs) Show and discuss a scatterplot with regression for the best-correlated pair, and one for the least-correlated pair. HdLngth HdLngth HdWidth Neck Length Chest Weight HdWidth 1 0.75 0.88 0.92 0.86 0.83 Neck 1 0.82 0.74 0.78 0.78 Length Chest Weight << fill in yellow cells 1 1 0.87 0.93 0.93 0.89 0.86 1 0.96 1 Least Correlated HeadWidth Vs Length 90 80 70 60 50 LENGTH Linear Regression for LENGTH 40 30 20 10 0 3 4 5 6 7 8 9 10 11 We can see that the points are not so close to the line. Therefore this correlation is not strong HeadWidth Vs Length 600 500 400 WEIGHT 300 Linear Regression for WEIGHT 200 100 0 15 20 25 30 35 40 45 50 55 60 We can see that the points are very close to the line. Therefore this correlation is very strong strong HEADWTH NECK LENGTH CHEST WEIGHT 11 16.5 15.5 17 15.5 13 15 13.5 13.5 12.5 16 9 12.5 14 11.5 13 13.5 9 13 16 12.5 13 13 10 16 10 13.5 13 13 14.5 9.5 13.5 14.5 11 11.5 13 16.5 14 13.5 15.5 11.5 12 15.5 9 14.5 13.5 10 10 11.5 11.5 11 10 15.5 12.5 5.5 9 8 10 6.5 7 7.5 8 7 6 9 4.5 4.5 5 5 8 7 4.5 6 9.5 5 5 5 4 6 4 6 5.5 6.5 5.5 4.5 6.5 6.5 5 5 7 6.5 5.5 6.5 7 6 6.5 7 5 7 8.5 4 5 5 5 4.5 4.5 8 8.5 16 28 31 31.5 22 21 26.5 27 20 18 29 13 10.5 21.5 17.5 21.5 24 12 19 30 19 20 17 13 24 13.5 22 17.5 21 20 16 28 26 17 17 21 27 24 21.5 28 16.5 19 28 15 23 23 15.5 15 17 15 13 10 30.5 18 53 67.5 72 72 62 70 73.5 68.5 64 58 73 37 63 67 52 59 64 36 59 72 57.5 61 54 40 63 43 66.5 60.5 60 61 40 64 65 49 47 59 72 65 63 70.5 48 50 76.5 46 61.5 63.5 48 41 53 52.5 46 43.5 75 57.3 26 45 54 49 35 41 41 49 38 31 44 19 32 37 29 33 39 19 30 48 32 33 28 23 42 23 34 31 34.5 34 26 48 48 29 29.5 35 44.5 39 40 50 31 38 55 27 44 44 26 26 30.5 28 23 24 54 32.8 80 344 416 348 166 220 262 360 204 144 332 34 140 180 105 166 204 26 120 436 125 132 90 40 220 46 154 116 182 150 65 356 316 94 86 150 270 202 202 365 79 148 446 62 236 212 60 64 114 76 48 29 514 140 Correlation Matrix HEADLEN HEADLEN 1 HEADWTH 0.75 NECK 0.88 LENGTH 0.92 CHEST 0.86 WEIGHT 0.83 HEADWTH 1 0.82 0.74 0.78 0.78 NECK 1 0.87 0.93 0.93 LENGTH 1 0.89 0.86 CHEST 1 0.96 WEIGHT 1 Stategize: Make an orderly list. Use function CORREL. Rank the correlations. Execute: HeadLength HeadLength HeadLength HeadLength HeadLength HeadWidth Least Correlated HeadWidth HeadWidth HeadWidth Neck Neck Neck Length Length Best Correlated Chest HeadWidth Neck Length Chest Weight Neck Length Chest Weight Length Chest Weight Chest Weight Weight 0.75 0.88 0.92 0.86 0.83 0.82 0.74 0.78 0.78 0.87 0.93 0.93 0.89 0.86 0.96 Problem 2 (25 points) It is easier to measure Head Length and Head Width than anything else. Using Head Length as the Explanatory variable, give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 12.95 for Head Length, predict each response variable. Which are you most / least confident about? Model C Most confident The R square and R in the length are the highest I confident that Least confident Model A The R square and R in the Weight are the smallest I confident that HEADLEN WEIGHT 11 16.5 15.5 17 15.5 13 15 13.5 13.5 12.5 16 9 12.5 14 11.5 13 13.5 9 13 16 12.5 13 13 10 16 10 13.5 13 13 14.5 9.5 13.5 14.5 11 11.5 13 16.5 14 13.5 15.5 11.5 12 15.5 9 14.5 13.5 10 10 11.5 11.5 11 10 15.5 12.5 80 344 416 348 166 220 262 360 204 144 332 34 140 180 105 166 204 26 120 436 125 132 90 40 220 46 154 116 182 150 65 356 316 94 86 150 270 202 202 365 79 148 446 62 236 212 60 64 114 76 48 29 514 140 NECK LENGTH CHEST 16 28 31 31.5 22 21 26.5 27 20 18 29 13 10.5 21.5 17.5 21.5 24 12 19 30 19 20 17 13 24 13.5 22 17.5 21 20 16 28 26 17 17 21 27 24 21.5 28 16.5 19 28 15 23 23 15.5 15 17 15 13 10 30.5 18 53 67.5 72 72 62 70 73.5 68.5 64 58 73 37 63 67 52 59 64 36 59 72 57.5 61 54 40 63 43 66.5 60.5 60 61 40 64 65 49 47 59 72 65 63 70.5 48 50 76.5 46 61.5 63.5 48 41 53 52.5 46 43.5 75 57.3 26 45 54 49 35 41 41 49 38 31 44 19 32 37 29 33 39 19 30 48 32 33 28 23 42 23 34 31 34.5 34 26 48 48 29 29.5 35 44.5 39 40 50 31 38 55 27 44 44 26 26 30.5 28 23 24 54 32.8 Problem 2 (25 points) HEADLEN WEIGHT It is easier to measure Head Length and Head Width than anything else. Using Head Length as the Explanatory variable , give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 12.95 for Head Length, predict each response variable. Which are you most / least confident about? Note: the regression equation is a linear equation of the form: y = m*x + b, where m is the slope and b is the y-intercept m and b are coefficients, and x and y are variables. Linear regression fits a line to the points, and determines the coefficients. Using the Excel regression tool in the Analysis Toolpak, the coefficients are given in the bottom table. StatCrunch regression provides the coefficients as intercept and slope Statdisk correlation and regression calls the coefficients y-intercept and slope DDXL simple regression refers to the y-intercept as the Constant coefficient y x value is 12.95 and you must calculate the predicted response variable y, for each of the 4 cases Explanatory variable Response variable HEADLEN WEIGHT SUMMARY OUTPUT Regression Statistics Multiple R 0.834185028 R Square 0.695864661 Adjusted R Square 0.690015904 Standard Error 67.81430364 Observations 54 ANOVA df Regression Residual Total Intercept HEADLEN SS MS F Significance F 1 547146.7848488 547146.8 118.9765 4.752016E-015 52 239136.5484846 4598.78 53 786283.3333333 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0%pper 95.0% U -430.98153 57.0305555603 -7.557028 6.41E-010 -545.4217118 -316.5413 -545.4217 -316.5413 47.3895677 4.344623307 10.90764 4.75E-015 38.6714432177 56.10769 38.67144 56.10769 182.7134 result x m b 12.95 47.38957 -430.9815 enter coeff's m and b 11 16.5 15.5 17 15.5 13 15 13.5 13.5 12.5 16 9 12.5 14 11.5 13 13.5 9 13 16 12.5 13 13 10 16 10 13.5 13 13 14.5 9.5 13.5 14.5 11 11.5 13 16.5 14 13.5 15.5 11.5 12 15.5 9 14.5 13.5 10 10 11.5 11.5 11 10 15.5 12.5 80 344 416 348 166 220 262 360 204 144 332 34 140 180 105 166 204 26 120 436 125 132 90 40 220 46 154 116 182 150 65 356 316 94 86 150 270 202 202 365 79 148 446 62 236 212 60 64 114 76 48 29 514 140 Problem 2 (25 points) HEADLEN NECK It is easier to measure Head Length and Head Width than anything else. Using Head Length as the Explanatory variable, give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 12.95 for Head Length, predict each response variable. Which are you most / least confident about? Note: the regression equation is a linear equation of the form: y = m*x + b, where m is the slope and b is the y-intercept m and b are coefficients, and x and y are variables. Linear regression fits a line to the points, and determines the coefficients. Using the Excel regression tool in the Analysis Toolpak, the coefficients are given in the bottom table. StatCrunch regression provides the coefficients as intercept and slope Statdisk correlation and regression calls the coefficients y-intercept and slope DDXL simple regression refers to the y-intercept as the Constant coefficient y x value is 12.95 and you must calculate the predicted response variable y, for each of the 4 cases Explanatory variable Response variable HEADLEN NECK SUMMARY OUTPUT Regression Statistics Multiple R 0.884806974 R Square 0.78288338 Adjusted R Square .778708061 0 Standard Error 2.653484621 Observations 54 ANOVA df Regression Residual Total Intercept HEADLEN SS MS F Significance F 1 1320.202340459 1320.202 187.5026 7.03E-019 52 366.1309928741 7.040981 53 1686.333333333 Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0%pper 95.0% U -9.59845131 2.2315307237 -4.301286 7.50E-005 -14.07635 -5.120557 -14.07635 -5.120557 2.327828979 0.1699994029 13.69316 7.03E-019 1.9867 2.668958 1.9867 2.668958 20.54693 result x m b 12.95 2.327829 -9.598451 enter coeff's m and b 11 16.5 15.5 17 15.5 13 15 13.5 13.5 12.5 16 9 12.5 14 11.5 13 13.5 9 13 16 12.5 13 13 10 16 10 13.5 13 13 14.5 9.5 13.5 14.5 11 11.5 13 16.5 14 13.5 15.5 11.5 12 15.5 9 14.5 13.5 10 10 11.5 11.5 11 10 15.5 12.5 16 28 31 31.5 22 21 26.5 27 20 18 29 13 10.5 21.5 17.5 21.5 24 12 19 30 19 20 17 13 24 13.5 22 17.5 21 20 16 28 26 17 17 21 27 24 21.5 28 16.5 19 28 15 23 23 15.5 15 17 15 13 10 30.5 18 Problem 2 (25 points) HEADLEN LENGTH It is easier to measure Head Length and Head Width than anything else. Using Head Length as the Explanatory variable, give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 12.95 for Head Length, predict each response variable. Which are you most / least confident about? Note: the regression equation is a linear equation of the form: y = m*x + b, where m is the slope and b is the y-intercept m and b are coefficients, and x and y are variables. Linear regression fits a line to the points, and determines the coefficients. Using the Excel regression tool in the Analysis Toolpak, the coefficients are given in the bottom table. StatCrunch regression provides the coefficients as intercept and slope Statdisk correlation and regression calls the coefficients y-intercept and slope DDXL simple regression refers to the y-intercept as the Constant coefficient y x value is 12.95 and you must calculate the predicted response variable y, for each of the 4 cases Explanatory variable Response variable HEADLEN LENGTH SUMMARY OUTPUT Regression Statistics Multiple R 0.919951335 R Square 0.84631046 Adjusted R Square .843354892 0 Standard Error 4.235234314 Observations 54 ANOVA df Regression Residual Total Intercept HEADLEN SS MS F Significance F 1 5136.220095677 5136.22 286.3444 8.50E-023 52 932.734904323 17.93721 53 6068.955 Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0%pper 95.0% U -0.8599962 3.5617525051 -0.241453 0.810154 -8.007175 6.287183 -8.007175 6.287183 4.591479335 0.2713365282 16.92171 8.50E-023 4.047003 5.135956 4.047003 5.135956 58.59966 result x m b 12.95 4.591479 -0.859996 enter coeff's m and b 11 16.5 15.5 17 15.5 13 15 13.5 13.5 12.5 16 9 12.5 14 11.5 13 13.5 9 13 16 12.5 13 13 10 16 10 13.5 13 13 14.5 9.5 13.5 14.5 11 11.5 13 16.5 14 13.5 15.5 11.5 12 15.5 9 14.5 13.5 10 10 11.5 11.5 11 10 15.5 12.5 53 67.5 72 72 62 70 73.5 68.5 64 58 73 37 63 67 52 59 64 36 59 72 57.5 61 54 40 63 43 66.5 60.5 60 61 40 64 65 49 47 59 72 65 63 70.5 48 50 76.5 46 61.5 63.5 48 41 53 52.5 46 43.5 75 57.3 Problem 2 (25 points) HEADLEN It is easier to measure Head Length and Head Width than anything else. Using Head Length as the Explanatory variable, give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 12.95 for Head Length, predict each response variable. Which are you most / least confident about? Note: the regression equation is a linear equation of the form: y = m*x + b, where m is the slope and b is the y-intercept m and b are coefficients, and x and y are variables. Linear regression fits a line to the points, and determines the coefficients. Using the Excel regression tool in the Analysis Toolpak, the coefficients are given in the bottom table. StatCrunch regression provides the coefficients as intercept and slope Statdisk correlation and regression calls the coefficients y-intercept and slope DDXL simple regression refers to the y-intercept as the Constant coefficient y x value is 12.95 and you must calculate the predicted response variable y, for each of the 4 cases Explanatory variable Response variable HEADLEN CHEST SUMMARY OUTPUT Regression Statistics Multiple R 0.862456042 R Square 0.743830424 Adjusted R Square .738904086 0 Standard Error 4.778503793 Observations 54 ANOVA df Regression Residual Total Intercept HEADLEN SS MS F Significance F 1 3447.732804026 3447.733 150.9905 5.31E-017 52 1187.3731219 22.8341 53 4635.105925926 Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0%pper 95.0% U -13.066495 4.0186319318 -3.251478 0.002018 -21.13047 -5.00252 -21.13047 -5.00252 3.761816627 0.306141888 12.28782 5.31E-017 3.147498 4.376135 3.147498 4.376135 35.64903 result x m b 12.95 3.761817 -13.0665 enter coeff's m and b CHEST 11 16.5 15.5 17 15.5 13 15 13.5 13.5 12.5 16 9 12.5 14 11.5 13 13.5 9 13 16 12.5 13 13 10 16 10 13.5 13 13 14.5 9.5 13.5 14.5 11 11.5 13 16.5 14 13.5 15.5 11.5 12 15.5 9 14.5 13.5 10 10 11.5 11.5 11 10 15.5 12.5 26 45 54 49 35 41 41 49 38 31 44 19 32 37 29 33 39 19 30 48 32 33 28 23 42 23 34 31 34.5 34 26 48 48 29 29.5 35 44.5 39 40 50 31 38 55 27 44 44 26 26 30.5 28 23 24 54 32.8 Problem 3 (25 points) Similar to problem 2, use Head Width as the Explanatory variable, and give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 6.19 for Head Width, predict each response variable. Which are you most / least confident about? Model B Most confident The R square and R in the neck are the highest I confident that Least confident Model C The R square and R in the length are the smallest I confident that HEADWTH WEIGHT NECK LENGTH CHEST 5.5 9 8 10 6.5 7 7.5 8 7 6 9 4.5 4.5 5 5 8 7 4.5 6 9.5 5 5 5 4 6 4 6 5.5 6.5 5.5 4.5 6.5 6.5 5 5 7 6.5 5.5 6.5 7 6 6.5 7 5 7 8.5 4 5 5 5 4.5 4.5 8 8.5 80 344 416 348 166 220 262 360 204 144 332 34 140 180 105 166 204 26 120 436 125 132 90 40 220 46 154 116 182 150 65 356 316 94 86 150 270 202 202 365 79 148 446 62 236 212 60 64 114 76 48 29 514 140 16 28 31 31.5 22 21 26.5 27 20 18 29 13 10.5 21.5 17.5 21.5 24 12 19 30 19 20 17 13 24 13.5 22 17.5 21 20 16 28 26 17 17 21 27 24 21.5 28 16.5 19 28 15 23 23 15.5 15 17 15 13 10 30.5 18 53 67.5 72 72 62 70 73.5 68.5 64 58 73 37 63 67 52 59 64 36 59 72 57.5 61 54 40 63 43 66.5 60.5 60 61 40 64 65 49 47 59 72 65 63 70.5 48 50 76.5 46 61.5 63.5 48 41 53 52.5 46 43.5 75 57.3 26 45 54 49 35 41 41 49 38 31 44 19 32 37 29 33 39 19 30 48 32 33 28 23 42 23 34 31 34.5 34 26 48 48 29 29.5 35 44.5 39 40 50 31 38 55 27 44 44 26 26 30.5 28 23 24 54 32.8 Problem 3 (25 points) Similar to problem 2, use Head Width as the Explanatory variable, and give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 6.19 for Head Width, predict each response variable. Which are you most / least confident about? HEADWTH This is similar to problem 2, except x value is 6.19 y 182.6084 result Explanatory variable Response variable HEADWTH WEIGHT SUMMARY OUTPUT Regression Statistics Multiple R 0.783483689 R Square 0.613846691 Adjusted R Square 0.606420666 Standard Error 76.4130867 Observations 54 ANOVA df Regression Residual Total Intercept HEADWTH SS MS F Significance F 1 482657.4227111 482657.4 82.66154 2.50E-012 52 303625.9106222 5838.96 53 786283.3333333 Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0%pper 95.0% U -208.002063 44.2332339819 -4.702393 1.93E-005 -296.7625 -119.2416 -296.7625 -119.2416 63.10347198 6.9406717194 9.091839 2.50E-012 49.176 77.03095 49.176 77.03095 x m b 6.19 63.10347 -208.0021 enter coeff's m and b WEIGHT 5.5 9 8 10 6.5 7 7.5 8 7 6 9 4.5 4.5 5 5 8 7 4.5 6 9.5 5 5 5 4 6 4 6 5.5 6.5 5.5 4.5 6.5 6.5 5 5 7 6.5 5.5 6.5 7 6 6.5 7 5 7 8.5 4 5 5 5 4.5 4.5 8 8.5 80 344 416 348 166 220 262 360 204 144 332 34 140 180 105 166 204 26 120 436 125 132 90 40 220 46 154 116 182 150 65 356 316 94 86 150 270 202 202 365 79 148 446 62 236 212 60 64 114 76 48 29 514 140 Problem 3 (25 points) Similar to problem 2, use Head Width as the Explanatory variable, and give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 6.19 for Head Width, predict each response variable. Which are you most / least confident about? HEADWTH This is similar to problem 2, except x value is 6.19 y 20.54198 result Explanatory variable Response variable HEADWTH NECK SUMMARY OUTPUT Regression Statistics Multiple R 0.818765163 R Square 0.670376393 Adjusted R Square 0.664037477 Standard Error 3.269483836 Observations 54 ANOVA df Regression Residual Total Intercept HEADWTH SS MS F Significance F 1 1130.478056606 1130.478 105.7557 3.92E-014 52 555.8552767274 10.68952 53 1686.333333333 Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0%pper 95.0% U 1.637905351 1.8926057008 0.865423 0.390782 -2.159886 5.435697 -2.159886 5.435697 3.053970437 0.296970257 10.28376 3.92E-014 2.458056 3.649885 2.458056 3.649885 x m 6.19 b 3.05397 1.637905 enter coeff's m and b NECK 5.5 9 8 10 6.5 7 7.5 8 7 6 9 4.5 4.5 5 5 8 7 4.5 6 9.5 5 5 5 4 6 4 6 5.5 6.5 5.5 4.5 6.5 6.5 5 5 7 6.5 5.5 6.5 7 6 6.5 7 5 7 8.5 4 5 5 5 4.5 4.5 8 8.5 16 28 31 31.5 22 21 26.5 27 20 18 29 13 10.5 21.5 17.5 21.5 24 12 19 30 19 20 17 13 24 13.5 22 17.5 21 20 16 28 26 17 17 21 27 24 21.5 28 16.5 19 28 15 23 23 15.5 15 17 15 13 10 30.5 18 Problem 3 (25 points) Similar to problem 2, use Head Width as the Explanatory variable, and give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 6.19 for Head Width, predict each response variable. Which are you most / least confident about? HEADWTH This is similar to problem 2, except x value is 6.19 y 58.59354 result Explanatory variable Response variable HEADWTH LENGTH SUMMARY OUTPUT Regression Statistics Multiple R 0.735446819 R Square 0.540882024 Adjusted R Square 0.532052832 Standard Error 7.320107107 Observations 54 ANOVA df Regression Residual Total Intercept HEADWTH SS MS F Significance F 1 3282.588661052 3282.589 61.26065 2.39E-010 52 2786.366338948 53.58397 53 6068.955 Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0%pper 95.0% U 26.38042856 4.2373894891 6.225632 8.46E-008 17.87748 34.88337 17.87748 34.88337 5.204056377 0.6648921352 7.826918 2.39E-010 3.869853 6.53826 3.869853 6.53826 x m b 6.19 5.204056 26.38043 enter coeff's m and b LENGTH 5.5 9 8 10 6.5 7 7.5 8 7 6 9 4.5 4.5 5 5 8 7 4.5 6 9.5 5 5 5 4 6 4 6 5.5 6.5 5.5 4.5 6.5 6.5 5 5 7 6.5 5.5 6.5 7 6 6.5 7 5 7 8.5 4 5 5 5 4.5 4.5 8 8.5 53 67.5 72 72 62 70 73.5 68.5 64 58 73 37 63 67 52 59 64 36 59 72 57.5 61 54 40 63 43 66.5 60.5 60 61 40 64 65 49 47 59 72 65 63 70.5 48 50 76.5 46 61.5 63.5 48 41 53 52.5 46 43.5 75 57.3 Problem 3 (25 points) Similar to problem 2, use Head Width as the Explanatory variable, and give regression equations for Neck, Length, Chest, Weight (as response variables), and provide each correlation value R (there will be 4) Using the value of 6.19 for Head Width, predict each response variable. Which are you most / least confident about? HEADWTH This is similar to problem 2, except x value is 6.19 y 35.64157 result Explanatory variable Response variable HEADWTH CHEST SUMMARY OUTPUT Regression Statistics Multiple R 0.778527096 R Square 0.60610444 Adjusted R Square .598529525 0 Standard Error 5.925414049 Observations 54 ANOVA df Regression Residual Total Intercept HEADWTH SS MS F Significance F 1 2809.358279923 2809.358 80.01469 4.22E-012 52 1825.747646003 35.11053 53 4635.105925926 Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0%pper 95.0% U 5.840762385 3.4300436925 1.702824 0.094572 -1.042124 12.72365 -1.042124 12.72365 4.814346282 0.5382108679 8.945093 4.22E-012 3.734347 5.894345 3.734347 5.894345 x m b 6.19 4.814346 5.840762 enter coeff's m and b CHEST 5.5 9 8 10 6.5 7 7.5 8 7 6 9 4.5 4.5 5 5 8 7 4.5 6 9.5 5 5 5 4 6 4 6 5.5 6.5 5.5 4.5 6.5 6.5 5 5 7 6.5 5.5 6.5 7 6 6.5 7 5 7 8.5 4 5 5 5 4.5 4.5 8 8.5 26 45 54 49 35 41 41 49 38 31 44 19 32 37 29 33 39 19 30 48 32 33 28 23 42 23 34 31 34.5 34 26 48 48 29 29.5 35 44.5 39 40 50 31 38 55 27 44 44 26 26 30.5 28 23 24 54 32.8 Problem 4 (25 points) Since 12.95 is average Head Length, and 6.19 is average Head Width, comment on the calculated responses in problems 2 and 3, and compare these responses with the average values of the data columns Neck, Length, Chest, Weight. (perhaps a table?) Could scientists use the Head Length and Head Width and a database of previous data to make reasonable predictions about other data for the bear population? Explain your point of view. average calc-P2 calc-P3 Neck Length Chest Weight 20.56 58.62 35.66 182.89 << enter averages from the respective data columns in Bears Data 20.55 58.60 35.65 182.71 << enter calculated values from problem 2 20.54 58.59 35.64 182.61 << enter calculated values from problem 3 As we can see the results are very similar to the real averages of the samples. This results happened because we use the averages of our explanatory variables Yes they can since we use a large sample and our models are pretty well predictors! We also need to worry about variation in actual bears vs. predicting the average WEIGHT NECK LENGTH CHEST 80 344 416 348 166 220 262 360 204 144 332 34 140 180 105 166 204 26 120 436 125 132 90 40 220 46 154 116 182 150 65 356 316 94 86 150 270 202 202 365 79 148 446 62 236 212 60 64 114 76 48 29 514 140 16 28 31 31.5 22 21 26.5 27 20 18 29 13 10.5 21.5 17.5 21.5 24 12 19 30 19 20 17 13 24 13.5 22 17.5 21 20 16 28 26 17 17 21 27 24 21.5 28 16.5 19 28 15 23 23 15.5 15 17 15 13 10 30.5 18 53 67.5 72 72 62 70 73.5 68.5 64 58 73 37 63 67 52 59 64 36 59 72 57.5 61 54 40 63 43 66.5 60.5 60 61 40 64 65 49 47 59 72 65 63 70.5 48 50 76.5 46 61.5 63.5 48 41 53 52.5 46 43.5 75 57.3 26 45 54 49 35 41 41 49 38 31 44 19 32 37 29 33 39 19 30 48 32 33 28 23 42 23 34 31 34.5 34 26 48 48 29 29.5 35 44.5 39 40 50 31 38 55 27 44 44 26 26 30.5 28 23 24 54 32.8

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