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Predicting Heights Project

Predicting Heights Project. By: Kristen Lawlor, Bridget Sanelli, and Katie Walsh. Three Measurements: Nearest ¼ Inch. Model One: Arm Span. Linear, Positive, Strong Outliers: High Leverage and Influential Points Correlation: 0.927 R 2 : 0.86 Ŷ=0.817(Arm Span)+12.5.

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Predicting Heights Project

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  1. Predicting Heights Project By: Kristen Lawlor, Bridget Sanelli, and Katie Walsh

  2. Three Measurements: Nearest ¼ Inch

  3. Model One: Arm Span • Linear, Positive, Strong • Outliers: High Leverage and Influential Points • Correlation: 0.927 • R2 : 0.86 • Ŷ=0.817(Arm Span)+12.5 • Linear model is a best fit • Scattered Residual Plot • Strong Correlation

  4. Model One: Arm Span Gender • Male: Linear, Positive, Strong • Correlation: 0.938 • R2: 0.88 • Ŷ=0.941(Arm Span)+4.2 • Female: Linear, Positive, Moderately Strong • Correlation: 0.8 • R2: 0.64 • Ŷ=0.577(Arm Span)+27.6

  5. Model Two: Knee Circumference • Linear, Positive, Moderate • Outliers due to Gender • Correlation: 0.5 • R2 : 0.25 • Ŷ=1.29(Knee)+47 • Linear model is a good fit, but not the best • Scattered Residual Plot • Moderate Correlation

  6. Model Two: Knee Gender • Male: Linear, Positive, Moderate • Correlation: 0.678 • R2: 0.46 • Ŷ=1.8(Knee)+42.65 • Female: Linear, Positive, Moderately Weak • Correlation: 0.346 • R2: 0.12 • Ŷ=0.487(Knee)+57.3

  7. Model Three: Leg • Linear, Positive, Strong • Outliers • Pink- High Leverage and Influential • Gray- Slightly Influential • Correlation: 0.843 • R2 : 0.71 • Ŷ=1.282(Leg)+16.6 • Linear model is a best fit • Scattered Residual Plot • Strong Correlation

  8. Model Three: Leg Gender • Male: Linear, Positive, Moderately Strong • Correlation: 0.762 • R2: 0.58 • Ŷ=1.635(Leg)+3.6 • Female: Linear, Positive, Moderately Strong • Correlation: 0.819 • R2: 0.67 • Ŷ=0.788(Leg)+34.7

  9. Kristen’s Residuals • Arm Span= 63.25” height=0.817(63.25)+12.5=64.175 63-64.175= -1.175” F. Height= .577(63.25)+27.6=64.095 63-64.095=-1.095” • Knee=13.25” height=1.29(13.25)+47=64.0925 63-64.0925=-1.0925” F. Height= .487(13.25)+57.3=63.753 63-63.753=-.753” • Leg Length= 35.50” • height=1.282(35.50)+16.6=62.111” • 63-62.111=.889” • F. Height=.788(35.50)+34.7=62.674 • 63-62.674=.326” • Arm Span predictions are overestimates • Knee predictions are overestimates • Leg Length predictions are underestimates

  10. Katie’s Residuals • Arm Span= 65” height=0.817(65)+12.5=65.605” 66-65.605= 0.395” F. Height= .577(65)+27.6=65.105” 66-65.105=0.895” • Knee=15” height=1.29(15)+47=66.35 66-66.35=-0.35” F. Height= .487(15)+57.3=64.605 66-64.605=1.395” • Leg Length= 40.50” • height=1.282(40.50)+16.6=68.521” • 66-68.521=-2.521” • F. Height=.788(40.50)+34.7=66.614 • 66-66.614=-0.614” • Arm Span predictions are underestimates • Knee prediction for: regular LSRL is overestimate , Female LSRL is underestimate • Leg Length predictions are overestimates

  11. Bridget’s Residuals • Arm Span= 66.5” height=0.817(66.5)+12.5=66.8305 67.75-66.8305= 0.9195” F. Height= .577(66.5)+27.6=65.9705 67.75-65.9705=1.7795” • Knee=15.5” height=1.29(15.5)+47=66.995 67.75-66.995=0.755” F. Height= .487(15.5)+57.3=64.8485 67.75-64.8485=2.9015” • Leg Length= 40” • height=1.282(40)+16.6=67.88” • 67.75-67.88=-0.13” • F. Height=.788(40)+34.7=66.22 • 67.75-66.22=1.53” • Arm Span predictions are underestimates • Knee predictions are underestimates • Leg Length prediction for: regular LSRL is overestimate, female LSRL is underestimate

  12. The Best Model: Arm Span • Correlation of 0.927 • Very scattered residual graph • Gender correlations strong and moderately strong • Smallest Residual when compared with actuals of Kristen, Katie and Bridget

  13. Prediction: Ms. Mattern NOT CONFIDENT • In order to predict Ms. Mattern’s height, we used the line of best fit model of the overall as well as the female line for each of the arm, knee, and leg measurements • ARM: • Overall - Ŷ= 0.817(69.5) + 12.5 = 69.3 inches • Female - Ŷ= 0.577 (69.5) + 27.6 = 67.7 inches • KNEE: • Overall - Ŷ= 1.29(17) + 47 = 68.93 inches • Female - Ŷ= 0.487(17) + 57.3 = 65.58 inches • Leg • Overall - Ŷ= 1.282(40.5) + 16.6 = 68.5 inches • Female - Ŷ= 0.788 (40.5) + 34.7 = 66.6 inches

  14. Prediction: Mr. Timmons CONFIDENT • In order to predict Mr. Timmons’ height, we used the line of best fit model of the overall as well as the male line for each of the arm, knee, and leg measurements • ARM: • Overall - Ŷ= 0.817(73.75) + 12.5 = 72.8 inches • Male - Ŷ= 0.941(73.75) + 47 = 73.6 inches • KNEE: • Overall – Ŷ= 1.29(14.75) + 47 = 66.0 inchesMale - Ŷ= 1.8(14.75) + 42.65 = 69.2 inches • LEG: • Overall - Ŷ= 1.282(39.5) + 16.6 = 67.2 inches • Male - Ŷ= 1.635(39.5) + 3.6 = 68.2 inches

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