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
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