Predicting Heights Project

Michelle Ji, Sam Shober, April Zhang

1. Shoulder to Floor

2. Head Circumference

3. Right Foot Length

6. Predictions

5. Group Members

7. Confidence

4. Best Model 8. Bias and Error

9. Conclusion

Introduction

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 inchesScatterplot/LSR

LineResidual Plot

Male/Female Difference

Shoulder to Floor Length

SCATTERPLOT AND LSR LINE

Positive Moderately strong Linear

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

Shoulder to Floor Length

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

SexF M

60

64

68

72

76

48 50 52 54 56 58 60 62 64

Shoulder_to_Floor

Height = 0.674Shoulder_to_Floor + 28.6; r2 = 0.79

Height = 0.948Shoulder_to_Floor + 15.4; r2 = 0.93

Collection 1 Scatter Plot

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 InchesScatterplot/LSR

LineResidual Plot

Male/Female Difference

Head Circumference

SCATTERPLOT AND LSR LINE

Linear Positive Moderately weak

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

Head Circumference

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

SexF M

60

64

68

72

76

20 21 22 23 24 25 26

Head_Circumference

Height = 0.0615Head_Circumference + 63.2; r2 = 0.00045

Height = 0.717Head_Circumference + 54.2; r2 = 0.093

Collection 1 Scatter Plot

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 inchesScatterplot/LSR

LineResidual Plot

Male/Female Difference

Right Foot Length

SCATTERPLOT/ LSR LINE

Linear Positive Moderate

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

Right Foot Length

FEMALE

Positive Weak

Smaller correlation: 0.2966

Linear Smaller

slope 1.15

MALE

Positive Moderate

Larger correlation: 0.6557

Linear Larger slope

1.9Sex

F M

60

64

68

72

76

8 9 10 11 12

Foot_Length

Height = 1.15Foot_Length + 54.4; r2 = 0.088

Height = 1.9Foot_Length + 51.4; r2 = 0.43

Collection 1 Scatter Plot

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

SexF M

60

64

68

72

76

48 50 52 54 56 58 60 62 64

Shoulder_to_Floor

Height = 0.674Shoulder_to_Floor + 28.6; r2 = 0.79

Height = 0.948Shoulder_to_Floor + 15.4; r2 = 0.93

Collection 1 Scatter Plot

Predictions and Residuals

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

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

Prediction of Teacher Heights

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

Prediction of Teacher Heights

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

Prediction of Teacher Heights

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

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.

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

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