Predicting Heights!By Julie Thein, Ricky Benner, and Brittany Bressler

Procedure

• We measured head size, shoulder width, and length of natural smile all in centimeters in order to determine which measurement best predicts a person’s height. – to measure height we had everybody stand against a tape

measure affixed to the white board– to measure head size we wrapped the tape measure right

above the supraorbital ridge and the below the atlas in the back of your head

– to measure shoulder width we held the tape measure at shoulder height and measured from tip to tip

– to measure length of natural smile we held the tape measure in front of an open smile and measured corner to corner

150

155

160

165

170

175

180

185

190

head

52 53 54 55 56 57 58 59

height = 3.03head - 2.2; r2 = 0.39

-10

0

10

20

52 53 54 55 56 57 58 59

head

Collection 1 Scatter Plot

Collection 1

head

height 0.625365

S1 = correlation

Form: linearDirection: positiveStrength: moderate

HEAD SIZE

150

155

160

165

170

175

180

185

190

smile

5.5 6.0 6.5 7.0 7.5 8.0

height = 4.19smile + 137; r2 = 0.11

-100

1020

5.5 6.0 6.5 7.0 7.5 8.0

smile

Collection 1 Scatter Plot

SMILE LENGTH

Collection 1

smile

height 0.335667

S1 = correlation

Form: linearDirection: positiveStrength: weak

SHOULDER WIDTH

150

155

160

165

170

175

180

185

190

shoulder

34 36 38 40 42 44 46 48 50

height = 2.1shoulder + 80; r2 = 0.63

-6

0

6

12

34 36 38 40 42 44 46 48 50

shoulder

Collection 1 Scatter Plot

Collection 1

shoulder

height 0.795282

S1 = correlation

Form: linearDirection: positiveStrength: moderately strong

HEAD SIZE

sexf m

150

155

160

165

170

175

180

185

190

head

52 53 54 55 56 57 58 59

height = 0.584head + 129; r2 = 0.031

height = 3.91head - 48.2; r2 = 0.20

Female Correlation Male Correlation

r= 0.176 r= 0.447

• Both positive, but male has a greater slope over female• Both linear• Males have a stronger correlation than females

SMILE LENGTH

sexf m

150

155

160

165

170

175

180

185

190

smile

5.5 6.0 6.5 7.0 7.5 8.0

height = 1.38smile + 152; r2 = 0.036

height = 4.46smile + 145; r2 = 0.19

Collection 1 Scatter Plot

Female Correlation Male Correlation

r= 0.19 r= 0.436

• Both positive, but male has a greater slope over female• Both linear• Males have a stronger correlation than females

SHOULDER WIDTH

sexf m

150

155

160

165

170

175

180

185

190

shoulder

34 36 38 40 42 44 46 48 50

height = 1.06shoulder + 119.3; r2 = 0.28

height = 1.994shoulder + 87.6; r2 = 0.55

Female Correlation Male Correlation

r= 0.529 r= 0.742

• Both positive, but male has a greater slope over female• Both linear• Males have a stronger correlation than females

BEST MODEL: SHOULDER!

• We chose the shoulder width model as the best predictor of height because they share the strongest correlation.

• Shoulder measurements most consistently changed in proportion to height while other measurements showed little to no correlation.

Residuals

• Ricky:

ŷ=2.1x+80ŷ=2.1(40)+80ŷ=164cmy=175175-164= 11

• Julie:

ŷ=2.1x+80ŷ=2.1(35)+80ŷ=153.5cmy=163163-153.5= 9.5

• BB:

ŷ=2.1x+80ŷ=2.1(40)+80ŷ=164cmy=162162-164= -2

Predictions

Mattern

ŷ=2.1x+80ŷ=2.1(45.5)+80ŷ=175.55cm

Timmins

ŷ=2.1x+80ŷ=2.1(47.5)+80ŷ=179.75cm

We are not very confident in these predictions. This is because our correlation was only moderately strong. Mrs. Mattern and Mr. Timmins are fully grown adults and our data only consisted of high school students. Mrs. Mattern would be considered a possible outlier for female shoulder widths; consequently, it might be extrapolation. For Mr. Timmins we have very little male data so it is difficult to predict his height accurately using a mostly female data set.

Bias & Errors

• BB’s v. Ricky’s measurements • Inconsistent shoulder and smile measuring

methods• Natural smile? • More females than males