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Predicting Heights

Predicting Heights. By: Chelsea Carleton, Colleen Kempf & Alex Coppola. Body Measurements. The three measurements that we collected were… Left wrist- around the wrist in inches Left ankle- around the ankle in inches with tape measurement

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Predicting Heights

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  1. Predicting Heights By: Chelsea Carleton, Colleen Kempf & Alex Coppola

  2. Body Measurements • The three measurements that we collected were… • Left wrist- around the wrist in inches • Left ankle- around the ankle in inches with tape measurement • Half arm span- from tip of middle finger of the right hand to the center of the sternum • All measurements were taken with a tape measure

  3. Height Vs. Left Ankle • Scatter Plot: • Linear, positive and moderately weak • Slightly influential outlierat (9, 75.5) & influential outlier with high leverage at (10, 75) • Residual Plot: • Slightly scattered with acurved pattern • Good Model? • This is not a good model for this date because although the scatter plot is linear, the correlation is low at 0.5, and the residual plot is slightly scattered with a curved pattern Predicted height= 39.1 + 3.06(actual ankle measurement) r= 0.5 r2= 0.25…25% of the change in height is due to the change in ankle size

  4. Height Vs. Left Ankle • Female: • Smaller heights • Lower correlation and coefficient of determination • Lower slope at 0.818 • 75% of the class is females • Male: • Bothoutliers are present • Taller heights • Higher correlation and coefficient of determination • Only 25% of the class is males • Steeper slope at 2.75 Female: Predicted height= 56.9 + 0.818(actual ankle measurement) r=0.228 r2=0.052…5.2% of the change in height is due to the change in ankle size Male: Predicted height= 45.4 + 2.75(actual ankle measurement) r=0.509 r2=0.26…26% of the change in height is due to the change in ankle size

  5. Height Vs. Left Wrist • Scatter Plot: • Linear, positive and moderately strong • Influential outliers at (7, 75) & (7, 75.5) • Residual Plot: • Scattered with a slight curve • Good Model? • This is a reasonable model because although the correlation is high at.866 and the scatter plot is linear, there is still a slight pattern in the residual plot. Predicted height= 25.5 + 6.65(actual wrist measurement) r= 0.866 r2= 0.75…75% of the change in height is due to the change in wrist size

  6. Height Vs. Left Wrist • Female: • Lower x-value & y-value points • Lower correlation and coefficient of determination • Lower slope at 4.24 • 75% of the class is females • Male: • Both outliers are males • Higher x-value & y-value points • Higher correlation and coefficient of determination • Only 25% of the class is males • Steeper slope at 7.74 Female: Predicted height= 39.3 + 4.24(actual wrist measurement) r= 0.6 r2= 0.36…36% of the change in height is due to the change in wrist size Male: Predicted height= 18.7 + 7.74(actual wrist measurement) r= 0.7416 r2=0.55…55% of the change in height is due to the change in wrist size

  7. Height Vs. Half of Arm Span • Scatter Plot: • Linear, positive andstrong • Influential outliers with slight high leverage at (38, 75) & (39, 75.5) • Residual Plot: • Scattered • Good Model? • This is our best model because the correlation is high at 0.927, the scatter plot is linear, and there is no pattern seen in the residual plot. Predicted height= 11.9 + 1.62(actual half of arm span measurement) r= 0.927 r2= 0.86…86% of the change in height is due to the change in half of the arm span length

  8. Height Vs. Half of Arm Span • Female: • Lower x-value & y-value points • Lower correlation and coefficient of determination • Lower slope at 1.297 • 75% of the class is females • Male: • Both outliers are males • Higher x-value & y-value points • Higher correlation and coefficient of determination • Only 25% of the class is males • Steeper slope at 1.352 Female: Predicted height= 22 + 1.297(actual half of arm span measurement) r= 0.781 r2= 0.61…61% of the change in height is due to the change in half the arm span length Male: Predicted height= 22 + 1.352(actual half of arm span measurement) r= 0.9 r2=0.81…81% of the change in height is due to the change in half the arm span length

  9. Residuals for group members • Chelsea: • y= 11.9 + 1.62(33) • Predicted height= 65.36 inches • Actual(66) – predicted(65.36) = 0.64 inches • F: y= 22 + 1.297(33) • Predicted height= 64.801 inches • Actual(66) – predicted(64.801) = 1.199 inches • Alex: • y= 11.9 + 1.62(31) • Predicted height= 62.12 inches • Actual(62) – predicted(62.12) = -0.12 inches • F: y= 22 + 1.297(31) • Predicted height= 62.207 inches • Actual(62) – predicted(62.207) = -0.207 • Colleen: • y= 11.9 + 1.62(31.5) • Predicted height= 62.93 inches • Actual(62) – predicted(62.93) = -0.93 inches • F: y= 22 + 1.297(31.5) • Predicted height= 62.8555 inches • Actual(62) – predicted(62.8555) = -0.8555inches • The general equation of y= 11.9 + 1.62x had more of an accuracy with our data.

  10. Prediction of Teacher’s Heights • Mrs. Mattern: • y= 11.9 + 1.62x • Predicted height= 11.9 +1.62(35.5) • Predicted height= 69.41 inches • Mr. Timmins: • y= 11.9 + 1.62x • Predicted height= 11.9 + 1.62(37) • Predicted height= 71.84 inches

  11. Prediction of Teacher’s Heights YES! We are confident in our predictions for the teacher’s heights because the inches measured for half of their arm span were not outliers in our graphs. Also, by looking at our residuals calculated, the LSRL correctly corresponds with the height of each person because the predicted value and the actual value are similar to one another.

  12. Errors/Bias • 25% of males in the class & 75% of females • Height: • Poor scale accuracy & determination • Shoes worn • Ankle: • Socks worn • 75% due to other factors • Wrist: • 25% due to other factors • Half Arm Span: • Unsure where the exact center of sternum • Angle of arm • Body position • 14% due to other factors

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