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Predicting Heights: Analyzing Relationships Between Body Measurements and Gender

This project investigates the correlation between various body measurements—such as lower leg height, wrist circumference, and arm length—and actual height, reflecting the differences in these relationships by gender. We compute linear regression models for each parameter, analyze correlation coefficients, and assess the model's fit through residual plots. Our findings highlight how these measurements can predict height, with detailed assessments of our predictions for two sets of subjects. We also address potential biases and conclude with insights from our analysis of statistical significance.

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Predicting Heights: Analyzing Relationships Between Body Measurements and Gender

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  1. Predicting heights project

  2. Introduction • Our group measured… • Arm length- From shoulder to farthest finger tip. • Wrist circumference- Wrapped tape measure around the subject’s wrist. • Lower Leg- (Had subject sit down) From top of knee to ankle. • Actual height and gender were also collected.

  3. Height vs. Lower Leg

  4. Height vs. Lower Leg • Describe graph (form, direction, strength) • Give correlation value (r) • LSR line • Interpret slope… • Interpret r-squared… • Describe residual plot (form, outliers) • Is the linear model appropriate? Use correlation, residual plot, and original plot

  5. GENDER VS. LOWER LEG

  6. FEMALES and Lower leg • FEMALES: • Describe female plot • List Female LSR line • List female correlation • List female r-squared • Describe female resid plot and comment on fit of linear model for females

  7. MALES & LOWER LEG • MALES: • Describe male plot • List male LSR line • List male correlation • List male r-squared • Describe male resid plot and comment on fit of linear model for males

  8. Compare male and female data

  9. Height Vs. Wrist Circumference

  10. Height Vs. Wrist Circumference • Describe graph (form, direction, strength) • Give correlation value (r) • HEIGHT = a + b(wrist circ) • Interpret slope… • Interpret r-squared… • Describe residual plot (form, direction, strength) • Is the linear model appropriate? Use correlation, residual plot, and original plot

  11. Height and Wrist Circumference Based on Gender • Same gender analysis as before • See slides 5 – 8

  12. Height vs. Arm Length

  13. Describe graph (form, direction, strength) • Give correlation value (r) • HEIGHT = a + b(arm length) • Interpret slope… • Interpret r-squared… • Describe residual plot (form, direction, strength) • Is the linear model appropriate? Use correlation, residual plot, and original plot

  14. Height and arm length based on gender • Same gender analysis as before • See slides 5 – 8

  15. Best OVERALL Model – Lower Leg • Justify choice

  16. Best Model for each gender • Justify choices

  17. Our Predicted Heights (use gender specific models) • Partner #1 • Lower leg measurement = 17.5 inches • Height = 21.2 + 2.68(17.5) = 68.1 inches • Actual Height = 64 inches • Residual = 64 – 68.1 = -4.1 inches • Overestimate • Partner #2 • Lower leg measurement = 18 inches • Height = 21.2 + 2.68(18) = 69.44 inches • Actual Height = 67 inches • Residual = 67 – 69.44 = -2.44 inches • Overestimate • Partner #3 • Lower leg measurement = 17.5 inches • Height = 21.2 + 2.68(17.5) = 68.1 inches • Actual Height = 71 inches • Residual = 71 – 68.1 = 2.9 • Underestimate

  18. Predicted teacher heights (use gender specific models) • Mrs. McNelis • Height = 2.68(17.5) + 21.2 = 68.1 inches • Mrs. Ladley • Height = 2.68(17.5) + 21.2 = 68.1 inches • Mr. Smith • Height = 5.2(17) + 10.4= 66.8 inches • Mrs. Tannous • Height = 2.68(17.5) + 21.2 = 68.1 inches • Miss Gemgnani • Height = 2.68(17.5) + 21.2 = 68.1 inches • Mrs. Bolton • Height = 2.68(17) + 21.2 = 66.8 inches

  19. Confidence • State how confident you are in your predictions of the guest teachers, and JUSTIFY WHY!

  20. Linreg t test (on best model) • Create linear model for best measurement and copy onto ppt

  21. Do linReg t test using the output above Ho: β1 = 0 Ha: β1 >, <, ≠ 0 Conditions (with graphs! Do not say “see previous slides”) & statement t = b1 – 0 = # SEb P(t > ______|df = n—2) = • We reject Ho…. • We have sufficient evidence… • Therefore…

  22. Lin Reg Confidence interval • Since we rejected Ho, we need to complete a conf. int. Statement b + t*(SEb) = (____, ____) We are 90% confident that for every 1 X variable unit increase, the Y variable increases btw ____ and ____ units on average.

  23. Analysis of gender heights Summary Stats: (do not copy this table from Fathom. Instead, type these on your slide neatly)

  24. 2 sample t test on the mean height of male/female Ho: μ males = μ females Ha: μ males ≠ μ females Conditions & statement t = mean1– mean2 = s12 + s22 n1 n2 2* P(t > _______| df = ___) = • We reject….. • We have sufficient evidence ….

  25. Confidence interval • If you reject Ho, complete an appropriate confidence interval

  26. Analysis of arm length by gender DO NOT put this type of table on your power point!! Write out the numbers neatly.

  27. 2 sample t test on the mean ARM LENGTH of male/female Ho: μ males = μ females Ha: μ males ≠ μ females Conditions & statement t = mean1– mean2 = s12 + s22 n1 n2 2* P(t > _______| df = ___) = • We reject….. • We have sufficient evidence ….

  28. Confidence interval • If you reject Ho, complete an appropriate confidence interval

  29. Bias and errors • List and explain possible sources of bias and error in your project.

  30. Conclusion • Make conclusions about ALL of your data analysis • Each measurement • Each test of significance and confidence interval • Overall conclusion about predicting heights Can be a bulleted list with explanation

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