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

2. Three Measurements: Nearest ¼ Inch Height Marked 60 inches on the white board Measured by placing a ruler on top of their heads to be able to mark their height Measured the height mark to the 60 in mark Added the 60 inches to the additional measure to find the height ERROR: with shoes on Arm Span Had each subject stretch their arms out on either side We measured from left middle finger to right middle finger Knee Measured circumference around the knee Knee cap around Gave each person option to do themselves or us measure ERROR: Thickness of pants Leg Had each person find their hip bones Measured from hip bone to floor ERROR: with shoes on

3. 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 Linear model is a best fit Scattered Residual Plot Strong Correlation

4. Model One: Arm Span Gender Male: Linear, Positive, Strong Correlation: 0.938 R 2 : 0.88 Ŷ=0.941(Arm Span)+4.2 Female: Linear, Positive, Moderately Strong Correlation: 0.8 R 2 : 0.64 Ŷ=0.577(Arm Span)+27.6

5. Model Two: Knee Circumference Linear model is a good fit, but not the best Scattered Residual Plot Moderate Correlation Linear, Positive, Moderate Outliers due to Gender Correlation: 0.5 R 2 : 0.25 Ŷ=1.29(Knee)+47

6. Model Two: Knee Gender Male: Linear, Positive, Moderate Correlation: 0.678 R 2 : 0.46 Ŷ=1.8(Knee)+42.65 Female: Linear, Positive, Moderately Weak Correlation: 0.346 R 2 : 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 R 2 : 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 R 2 : 0.58 Ŷ=1.635(Leg)+3.6 Female: Linear, Positive, Moderately Strong Correlation: 0.819 R 2 : 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 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 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 NOT CONFIDENT

14. Prediction: Mr. Timmons 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 inches Male - 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 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 inches Male - 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 CONFIDENTCONFIDENT