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Predicting Heights Project

Michelle Ji , Sam Shober , April Zhang. Predicting Heights Project. Introduction. 1. Shoulder to Floor. 5. Group Members. 2. Head Circumference. 6. Predictions. 3. Right Foot Length. 7. Confidence. 4. Best Model. 8. Bias and Error. 9. Conclusion. Shoulder to Floor Length Intro.

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Predicting Heights Project

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  1. Michelle Ji, Sam Shober, April Zhang Predicting Heights Project

  2. Introduction 1. Shoulder to Floor 5. Group Members 2. Head Circumference 6. Predictions 3. Right Foot Length 7. Confidence 4. Best Model 8. Bias and Error 9. Conclusion

  3. Shoulder to Floor Length Intro. • Ticks pre-marked on wall • Participants take of both shoes and stand with feet as close to wall as possible • Observer approximates which tick the participants’ shoulder reached • Measured in inches Scatterplot/LSR Line Residual Plot Male/Female Difference

  4. Shoulder to Floor Length Scatterplot and LSR Line Positive Moderately strong Linear

  5. Shoulder to Floor Length Residual Plot Scattered LSR Line a good fit r = 0.943398 r2 = 0.89 89% of the variation in height is explained by the variation in shoulder to floor length

  6. Shoulder to Floor Length Female Male Positive Strong Larger correlation: 0.9644 Linear Larger Slope 0.948 Generally larger values • Positive • Moderately Strong • Smaller correlation: 0.8888 • Linear • Smaller Slope • 0.674 • Generally smaller values

  7. Head Circumference Intro. • Participants lifted hair about head (for long hair) • Tape measurer placed as tightly as possible around head above ears • Measurement read as point where tick and metal tip met • Measured in Inches Scatterplot/LSR Line Residual Plot Male/Female Difference

  8. Head Circumference Scatterplot and LSR Line Linear Positive Moderately weak

  9. Head Circumference Residual Plot Slight Horn Shape LSR Line not best fit Outlier near 26 r = 0.42426 r2 = 0.18 18% of the variation in height is explained by the variation in head circumference

  10. Head Circumference Female Male Positive Weak Larger correlation: 0.305 Linear Larger slope 0.71 Outlier: near 26 • Positive • Weak • Smaller correlation: 0.02 • Linear • Smaller Slope • 0.0615

  11. Right Foot Length Intro. • Participants made to take off their right shoe • They were to line the heel of their foot to the end of the ruler • Observer approximated the tick on the ruler that the participants foot touched (looked at the longest toe) • Measured in inches Scatterplot/LSR Line Residual Plot Male/Female Difference

  12. Right Foot Length Scatterplot/ LSR Line Linear Positive Moderate

  13. Right Foot Length Residual Plot Scattered LSR Line is a good fit Two possible outliers Near 11.5 and 12 r = 0.76811 r2 = 0.59 59% of the variation in height is explained by the variation right foot length

  14. Right Foot Length Female Male Positive Moderate Larger correlation:0.6557 Linear Larger slope 1.9 • Positive • Weak • Smaller correlation: 0.2966 • Linear • Smaller slope • 1.15

  15. Best Model • Shoulder to Floor Length • Strongest correlation: r = 0.9434 • Female: r = 0.8888 • Male: r = 0.9644 • r2 = 0.89 • Female: r2= 0.79 • Male: r2= 0.93

  16. Predictions and Residuals Michelle Sam Shoulder to Floor: 57 inches Height=.674(57) +28.6 = 67.018 inches Actual Height= 67 inches Residual =67-67.018= -.018 inches • Shoulder to Floor: 50 inches • Height=.674(50) +28.6 = 59.3 inches • Actual Height= 63 inches • Residual =63-59.3= 3.7 inches

  17. Predictions and Residuals April • Shoulder to Floor: 53 inches • Height=.674(53) +28.6 = 64.322 inches • Actual Height= 64 inches • Residual =64-64.322= -.322 inches

  18. Prediction of Teacher Heights Mr. Lake Ms. gemgnani Shoulder to Floor: 55 inches Height=.674(55) +28.6 = 65.67 inches • Shoulder to Floor: 59 inches • Height= .948(59) + 15.4 = 71.332 inches

  19. Prediction of Teacher Heights Mr. Walsh Miss. tannous Shoulder to Floor: 56.5 inches Height=.674(56.5) +28.6 = 66.681 inches • Shoulder to Floor: 56 inches • Height= .948(56) + 15.4 = 68.488 inches

  20. Prediction of Teacher Heights Mrs. robinson Ms. arden Shoulder to Floor: 53.5 inches Height= .674(53.5) + 28.6 = 64.659 • Shoulder to Floor: 58 inches • Height=.674(58) +28.6 = 67.692 inches

  21. Confidence We are confident in our predictions because our data has a moderately strong linear shape and our LSR line has a strong correlation, especially for the males. By using different models for females and males, we eliminate a possible lurking variable, making us even more confident in our predictions. In addition, our model accurately predicted our own heights. Sam and April’s residuals were very small, but Michelle’s was a little larger, but not large enough to make us less confident in our models.

  22. Bias and Error • Measurements taken by different observers • Michelle more exact than Sam on foot measurements • Variation in tightness of tape between April and Michelle • Tightness of tape when measuring head circumference • Amount of hair in tape measurer when measuring head circumference • Exact location of measurement for head circumference • Tried to place it in the same place, can’t be exact • Participants may have placed foot more forward or back than others on foot length measurement • Potential slouching during shoulder to floor measurement • Human error during measurements • Hard to approximate

  23. Conclusion • Shoulder to floor length was best predictor • Greatest correlation, strongest, most linear, lowest residuals out of all three • Females have lower correlation for all three types of measurements • Females had smaller measurements than males • With the exception of head circumference • Head circumference had little correlation to height • Future: • Measure adults • Make sure all participants have good posture • Use more advanced equipment • Height and foot measurer • Measure height to nearest mm • Be more accurate on foot length

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