BODY MEASUREMENTS Kathy, Sarah and Tyler

INTRODUCTION We chose to measure:

Hip-to-knee length Head-nose circumference Top of palm

We measured in quarter inches

MEASUREMENTS: HEIGHT

We based our measurement of height based on a scale marked on the white board

Each subject was then measured off the scale with a book as a guide

MEASUREMENTS: HIP TO KNEE

We decided that a femur was a good measurement of height

The closest measurement possible is from the top of the hipbone to the middle of the knee when bent

We asked subjects to identify top of hip and then bend knee

MEASUREMENTS: HEAD-NOSE CIRCUMFERENCE

For our circumference, we measured around the head at the tip of the nose

Subjects held the tape at the nose while we measures around

MEASUREMENTS: TOP OF PALM

In order to measure the length of the palm, subjects bent wrist and knuckles and measurement was taken from wrist bone to middle finger knuckle

Measurements were taken in quarter inches

SCATTER PLOT OF HIP TO KNEE

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HiptoKnee16 18 20 22 24 26 28 30

Height = 1.463HiptoKnee + 35.4; r2 = 0.59

Collection 1 Scatter Plot

Collection 1Height

HiptoKnee 0.767435S1 = correlation

•The form of the scatter plot is roughly linear with a positive association. The strength is moderately strong with r = 0.767435.•The r2 of 0.59 shows that 59% of the variability in height is attributed to the variability in hip to knee length.

SCATTER PLOT OF HIP TO KNEE BY GENDER

Genderf m

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HiptoKnee16 18 20 22 24 26 28 30

Height = 1.304HiptoKnee + 37.3; r2 = 0.63Height = 0.636HiptoKnee + 55.8; r2 = 0.28

Collection 1 Scatter Plot

• The two LSR lines vary between the genders •For females (the lower line), the correlation is stronger than the males (the upper line), with r’s of 0.79 and 0.53, respectively. •Both have a moderately strong association with linear qualities •The males show a steeper line than the females, and both show a positive association

Female: r = 0.793725Male: r= 0.529150

RESIDUAL PLOT OF HIP TO KNEE

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HiptoKnee16 18 20 22 24 26 28 30

Height = 1.463HiptoKnee + 35.4; r2 = 0.59

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16 18 20 22 24 26 28 30HiptoKnee

Collection 1 Scatter Plot

• The residual plot (lower plot) for the hip to knee data shows no obvious patterns, showing that our LSRL fit our data

r = 0.768115r2 = 0.59

SCATTER PLOT OF NOSE-HEAD CIRCUMFERENCE

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NoseHead19 20 21 22 23 24 25

Height = 0.102NoseHead + 64.7; r2 = 0.0013

Collection 1 Scatter Plot

Collection 1HiptoKnee

NoseHead -0.15286S1 = correlation

• The form of nose-head circumference and height shows hardly any form or direction, with a very slight negative association. The form is scattered. The strength is weak, show by the correlation of -0.15286.•Our r2 of 0.0013 shows that .13% of the variability in height is attributed to the variability in nose-head circumference.

SCATTER PLOT OF NOSE-HEAD CIRCUMFERENCE BY GENDER

Genderf m

5658606264666870727476

NoseHead19 20 21 22 23 24 25

Height = -0.0102NoseHead + 64.2; r2 = 0.000036Height = 0.0821NoseHead + 68.6; r2 = 0.0019

Collection 1 Scatter Plot

• The scatter plot broken down by gender shows a difference in head circumference between males and females; yet, the form of both LSR lines were similar in their positive direction, weak scatter form, and weak strength. The males had the higher line while the females the lower.

Females: r = 0.006Males: r = 0.04359

RESIDUAL PLOT OF NOSE-HEADCIRCUMFERENCE

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NoseHead19 20 21 22 23 24 25

Height = 0.102NoseHead + 64.7; r2 = 0.0013

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19 20 21 22 23 24 25NoseHead

Collection 1 Scatter Plot

• The residual plot shows granularity which means that the model of the LSRL does not fit our data.

r2 = 0.0013r = 0.03606

SCATTER PLOT OF PALM LENGTH

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Palm3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2

Height = 6.47Palm + 41.7; r2 = 0.36

Collection 1 Scatter Plot

Collection 1Height

Palm 0.600379S1 = correlation

•The form is clustered at each data point with a slight linear association. The direction is positive while the strength is moderate. Our correlation is 0.600379•Our r2 of 0.36 shows that 36% of the variability in height is attributed to the variability in palm length.

SCATTER PLOT OF PALM LENGTH BY GENDER

Genderf m

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Palm3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2

Height = 2.3Palm + 55.5; r2 = 0.071Height = 4.07Palm + 53.7; r2 = 0.38

Collection 1 Scatter Plot

• Our scatter plot of palm length broken down by gender has two LSR lines, with the males having the higher line and the females the lower.•The male’s data was linear with a positive association. The data was moderately strong with a correlation of 0.616.•The female’s data was slightly linear with a positive association. The data was moderately weak with a correlation of 0.266.•The male’s data LSRL was more reliable than the female’s.

Males: r = 0.616441Females: r = 0.26646

RESIDUAL PLOT OF PALM LENGTH

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Palm3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2

Height = 6.47Palm + 41.7; r2 = 0.36

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3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2Palm

Collection 1 Scatter Plot

• The residual plot for palm length shows obvious granularity in the stair step appearance. This shows that our LSR line does not fit the data.

r2 = 0.36r = 0.6

BEST MODEL The LSRL chosen by our group was the hip-to-

knee because it had the highest correlation for both genders

We will base the female teachers off of the LSRL created by only the female data but approximate the male data off of the LSRL created by both the male and female data for better accuracy

Female: height = 1.304(hip-to-knee) + 37.3 Male: height = 1.463(hip-to-knee) + 35.4

PREDICTIONS OF GROUP MEMBERS Kathy: Female model used with hip-to-knee

measurement of 18” gave height of 60.772” which was 2.228” away from her actual height of 63”

Sarah: Female model used with 21” hip-to-knee length gave height as 64.684” which was 1.316” away from the actual height of 66”

Tyler: Total model used with hip-to-knee measurement of 23” gave height of 69.049” which was 3.451” away from actual height of 72.5”

Our models were consistently short

PREDICTIONS OF TEACHERS Ms. Tannous: 1.304(21) + 37.3 =

64.684” Ms. Arden: 1.304(22) + 37.3 = 65.988” Mrs. Robinson: 1.304(21) + 37.3 =

64.684” Mr. Lake: 1.463(23) + 35.4 = 69.049” Mr. Walsh: 1.463(21) + 35.4 = 66.123”

CONFIDENCE OF PREDICTIONS For ourselves, our models were overall

short, and therefore we can presume that our estimations for the teachers may also fall short from their real heights.

BIAS AND ERROR Some subjects felt

awkward with measuring the top of the hipbone

Our other two measurements showed too uniform of distributions to be useful

We did not specify shoes or no shoes for everyone

Some subjects may not have correctly identified the top of their hipbone

Cargo pants were difficult to find the top of knee

CONCLUSION The measurement of

hip-to-knee was the most reliable compared with the measurement of the palm and of the head over the nose.

Our predictions seemed to fall slightly short, suggesting that the measuring the femur through the hipbone is not as reliable.

Our female data for the hip-to-knee measurement had the highest correlation, followed by the LSRL for both genders that we used for males.