1. Michelle Ji, Sam Shober, April Zhang

2. 1. Shoulder to Floor 2. Head Circumference 3. Right Foot Length 6. Predictions 5. Group Members 7. Confidence 4. Best Model8. Bias and Error 9. Conclusion

3.  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 LineResidual Plot Male/Female Difference

4. SCATTERPLOT AND LSR LINE  Positive  Moderately strong  Linear

5. RESIDUAL PLOT  Scattered  LSR Line a good fit  r = 0.943398  r 2 = 0.89  89% of the variation in height is explained by the variation in shoulder to floor length

6. FEMALE  Positive  Moderately Strong  Smaller correlation: 0.8888  Linear  Smaller Slope  0.674  Generally smaller values MALE  Positive  Strong  Larger correlation: 0.9644  Linear  Larger Slope  0.948  Generally larger values

7.  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 LineResidual Plot Male/Female Difference

8. SCATTERPLOT AND LSR LINE  Linear  Positive  Moderately weak

9. RESIDUAL PLOT  Slight Horn Shape  LSR Line not best fit  Outlier near 26  r = 0.42426  r 2 = 0.18  18% of the variation in height is explained by the variation in head circumference

10. FEMALE  Positive  Weak  Smaller correlation : 0.02  Linear  Smaller Slope  0.0615 MALE  Positive  Weak  Larger correlation: 0.305  Linear  Larger slope  0.71  Outlier: near 26

11.  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 LineResidual Plot Male/Female Difference

12. SCATTERPLOT/ LSR LINE  Linear  Positive  Moderate

13. RESIDUAL PLOT  Scattered  LSR Line is a good fit  Two possible outliers  Near 11.5 and 12  r = 0.76811  r 2 = 0.59  59% of the variation in height is explained by the variation right foot length

14. FEMALE  Positive  Weak  Smaller correlation : 0.2966  Linear  Smaller slope  1.15 MALE  Positive  Moderate  Larger correlation: 0.6557  Linear  Larger slope  1.9

15.  Shoulder to Floor Length  Strongest correlation: r = 0.9434  Female: r = 0.8888  Male: r = 0.9644  r 2 = 0.89  Female: r 2 = 0.79  Male: r 2 = 0.93

16. MICHELLE  Shoulder to Floor: 50 inches  Height=.674(50) +28.6 = 59.3 inches  Actual Height= 63 inches  Residual =63-59.3= 3.7 inches SAM  Shoulder to Floor: 57 inches  Height=.674(57) +28.6 = 67.018 inches  Actual Height= 67 inches  Residual =67-67.018= -.018 inches

17. 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. MR. LAKE  Shoulder to Floor: 59 inches  Height=.948(59) + 15.4 = 71.332 inches MS. GEMGNANI  Shoulder to Floor: 55 inches  Height=.674(55) +28.6 = 65.67 inches

19. MR. WALSH  Shoulder to Floor: 56 inches  Height=.948(56) + 15.4 = 68.488 inches MISS. TANNOUS  Shoulder to Floor: 56.5 inches  Height=.674(56.5) +28.6 = 66.681 inches

20. MRS. ROBINSON  Shoulder to Floor: 58 inches  Height=.674(58) +28.6 = 67.692 inches MS. ARDEN  Shoulder to Floor: 53.5 inches  Height=.674(53.5) + 28.6 = 64.659

21. 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.  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.  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