1. 1 University of Pune By:Motilal & Jyoti Nevgi (University of Pune,Pune)

2. 2 Aim : - To check whether Indians are getting taller and to predict the height of the tallest Indian (Male/Female) in 2020. Formulation of the problem 1. Paired t-test 2. Trend Analysis 3. Prediction of the Tallest Indian

3. 3 Major States in each stratum: - 1. East : West Bengal, Assam, Arunachal Pradesh, Tripura, and Manipur. 2. West : Maharashtra, Gujarat and Rajasthan. 3. North : Jammu & Kashmir, Himachal Pradesh, Punjab, Haryana and U.P. 4. South : Kerala, Tamilnadu, Karnataka and Andhra Pradesh. 5. Center : Madhya Pradesh, Bihar, Orissa and Chhatisgarh Sampling Technique Population is all the Indians aged from 20-30 years. Divide it into 5 strata namely East, West, North, South & Center. Used stratified sampling with proportional allocation.

4. 4 Data Collection Data are collected from 3 sources. Sample size From Hostel & Camp: Male – 136Female – 55 From Matrimonial: Sample size in each year is 40 for each gender for 21 years (Male & Female). 3. Matrimonial Website www.shaadi.com 1. Hostel (University of Pune, Pune) 2. National Youth Integration Camp (Held at University of Pune, Pune)

5. 5 Statistical Analysis Normality Testing Multiple Linear Regression Paired t-test Trend Analysis Prediction of the Tallest Indian

6. 6 Male Candidate Conclusion : Since p value > 0.05, hence data are normally distributed.

7. 7 Female Candidate Conclusion : Since p value > 0.05, hence data are normally distributed.

8. 8 Matrimonial Data Conclusion : Since p value > 0.05, hence data are normally distributed.

9. 9 Multiple Linear Regression Model: Y M = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 4 + ε Where, Y M = Adult height of an Indian male X 1 = Height of his father X 2 = Height of his mother X 3 = Height of his grand-father X 4 = Height of his grand-mother Hypotheses: 1. H 0 : β 1 = 0 Vs H 1 : β 1  0 2. H 0 : β 2 = 0 Vs H 1 : β 2  0 3. H 0 : β 3 = 0 Vs H 1 : β 3  0 4. H 0 : β 4 = 0 Vs H 1 : β 4  0 Male Candidate

10. 10 Best Subset Selection Reduced Model: Y M = β 0 + β 1 X 1 + β 2 X 2 + β 4 X 4 + ε g g r r f m a a a o n n t t d d h h e e m f Vars R-Sq R-Sq(adj) C-p S r r o a 1 16.2 15.6 16.4 6.7516 X 1 13.3 12.6 21.6 6.8693 X 2 20.8 19.6 10.3 6.5909 X X 2 16.8 15.6 17.2 6.7515 X X 3 25.4 23.7 4.1 6.4198 X X X 3 21.0 19.2 11.9 6.6061 X X X 4 26.0 23.8 5.0 6.4167 X X X X

11. 11 Regression Equation Adult Male = 91.9+0.314 father+0.355 mother-0.192 grand mother Conclusion : - β 0, β 1, β 2, and β 4 are significant at 5% l.o.s. Predictor Coef SE Coef T P Constant 91.90 13.88 6.62 0.000 father 0.31355 0.07940 3.95 0.000 mother 0.35522 0.09129 3.89 0.000 grand mthr -0.19245 0.06728 -2.86 0.005 Regression Analysis

12. 12 Based on regression equation average height of adult male in 2020 will be 172.17 Cms. Confidence Interval 95% Confidence Interval for estimated average height of adult male is (In Cms.) ( 171.09, 173.25 ) Estimation of Average Height

13. 13 Multicollinearity Male Candidate Adult Male father mother Grand-mother Father 0.403 Mother 0.364 0.426 Grand-mother 0.060 0.331 0.573 Grand-father 0.235 0.404 0.296 0.305 Cell Contents: Pearson correlation

14. 14 Test for Multicollinearity Eigen values Analysis Male Candidate λ’ = 0.6918 0.4137 1.8945 1.0000 0.4261 0.3310 0.4261 1.0000 0.5730 0.3310 0.5730 1.0000 X’X = Eigen values of X’X λ max λ min Conditional No. = = = 4.5794 Conclusion: - Since Conditional No <10, multicollinearity does not exist.

15. 15 Female Candidate Model: Y F = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 4 + ε Where, Y F = Adult height of an Indian female X 1 = Height of her mother X 2 = Height of her father X 3 = Height of her grand-mother X 4 = Height of her grand-father Hypotheses: 1. H 0 : β 1 = 0 Vs H 1 : β 1  0 2. H 0 : β 2 = 0 Vs H 1 : β 2  0 3. H 0 : β 3 = 0 Vs H 1 : β 3  0 4. H 0 : β 4 = 0 Vs H 1 : β 4  0

16. 16 Best Subset Selection Reduced Model: Y F = β 0 + β 2 X 2 + β 3 X 3 + β 4 X 4 + ε f m g g a o r r t t a a h h n n e e d d r r _ _ m f Vars R-Sq R-Sq(adj) C-p S 1 1 o a 1 28.6 27.2 10.1 4.5659 X 1 27.7 26.3 10.8 4.5950 X 2 36.7 34.2 5.2 4.3414 X X 2 34.9 32.4 6.7 4.4011 X X 3 39.8 36.2 4.5 4.2744 X X X 3 39.3 35.8 4.9 4.2896 X X X 4 41.5 36.9 5.0 4.2536 X X X X

17. 17 Conclusion : -β 0, β 2, β 3, and β 4 are significant at 5% l.o.s. Regression Equation Adult Female = 49.5+0.178 fthr+0.316 grnd mthr+0.189 grnd fthr Predictor Coef SE Coef T P Constant 49.46 22.53 2.20 0.033 father 0.1780 0.1095 2.63 0.010 grand mthr 0.3161 0.1556 2.03 0.047 grand fthr 0.18879 0.08420 2.24 0.029 Regression Analysis

18. 18 Based on regression equation average height of adult female in 2020 will be 161.34 Cms Confidence Interval 95% Confidence Interval for estimated average height of adult female is (In Cms.) ( 160.21, 162.47 ) Estimation of Average Height

19. 19 Female Candidate Adult Female father mother Grand-mother Father 0.535 Mother 0.393 0.383 Grand-mother 0.441 0.439 0.431 Grand-father 0.562 0.612 0.257 0.293 Cell Contents: Pearson correlation Multicollinearity

20. 20 Female Candidate 1.0000 0.4391 0.6122 0.4391 1.0000 0.2931 0.6122 0.2931 1.0000 X’X = Conclusion: - Since Conditional No <10, multicollinearity does not exist. Eigen values of X’X λ’ = 0.7281 0.3626 1.9093 λ max λ min Conditional No. == 5.2656 Test for Multicollinearity Eigen values Analysis

21. 21 Paired t-test Let, X 1 = Height of an adult son Y 1 = Height of his father Z 1 = Height of his grand father X 2 = Height of an adult daughter Y 2 = Height of her mother Z 2 = Height of her grand mother Hypotheses: 1. H 0 : E(X 1 ) = E(Y 1 ) Vs H 1 : E(X 1 ) > E(Y 1 ) 2. H 0 : E(Y 1 ) = E(Z 1 ) Vs H 1 : E(Y 1 ) > E(Z 1 ) 3. H 0 : E(X 2 ) = E(Y 2 ) Vs H 1 : E(X 2 ) > E(Y 2 ) 4. H 0 : E(Y 2 ) = E(Z 2 ) Vs H 1 : E(Y 2 ) > E(Z 2 ) 5. H 0 : E(X 2 ) = E(Z 2 ) Vs H 1 : E(X 2 ) > E(Z 2 )

22. 22 Pairt-Valuep-Value Adult Male & Father2.720.004 Father & Grand-Father1.900.030 Adult Male & Grand-Father3.930.000 Adult Female & Mother2.340.011 Adult Female & Grand Mother 5.410.000 Samplest-Valuep-Value Mother & Grand-Mother1.860.033

23. 23 Generation wise prediction Conclusion :- Conclusion :- Based on above graph predicted average height of adult male in 2020 will be 172.06 cm. Male candidate Confidence Interval (In Cms) : - ( 172.04, 172.07 )

24. 24 :- B Conclusion :- Based on the above graph predicted average height of adult female candidate in 2020 will be 162.22cms. Female candidate Confidence Interval (In Cms) : - ( 162.21, 162.23 )

25. 25 Trend Analysis Male Candidate Interpretation : - In above graph we observe there is increasing linear trend, which shows increase in average height.

26. 26 Test for β = 0 Predictor Coef SE Coef T P Constant 170.750 0.609 280.43 0.000 Time 0.164 0.04849 3.39 0.006 H 0 : β = 0 Vs H 1 : β > 0 Hypothesis Conclusion : - Regression coefficient β is significant at 5% level of Significance.

27. 27 Prediction of Average Height for 2020 Male Candidate Conclusion :- Average height of adult male in 2020 will be 176.83 Cms. Confidence Interval (In Cms) : - ( 176.13, 177.53 )

28. 28 Female Candidate Interpretation :- In above graph we observe there is increasing linear trend, which shows increase in average height.

29. 29 Test for β = 0 Predictor Coef SE Coef T P Constant 159.583 0.575 277.66 0.000 Time 0.114 0.04577 2.49 0.044 H 0 : β = 0 Vs H 1 : β > 0 Hypothesis Conclusion :- Regression coefficient β is marginally significant at 5% level of Significance.

30. 30 Prediction of Average Height for 2020 Female Candidate Conclusion :- Average height of adult female in 2020 will be 163.81 Cms. Confidence Interval (In Cms) :- ( 163.19, 164.43 )

31. 31 Prediction of Tallest Indian Conclusion : - Height of the tallest Indian male in 2020 will be 195.58 Cms. Male candidate

32. 32 Prediction of Tallest Indian Conclusion : - Height of the tallest Indian female in 2020 will be 185.42 Cms. Female candidate

33. 33 Conclusions 1. 1.Indians are getting taller. 2. Predicted average height in year 2020 (a) Male: 176.83 cms, Female: 163.81 cms (From Matrimonial Data) (b) Male: 172.17 cms, Female: 161.34 cms (From Regression Analysis) (c) Male: 172.06 cms, Female: 162.22 cms (Generation wise) 3. Predicted height of the tallest Indian in year 2020 will be 195.58 cms. 4. Generation wise average rate of increase in height 4.1 Male (a) Grand Father to Father: 1.49 cms. (b) Father to Male Child: 1.93 cms. 4.2 Female (a) Grand Mother to Mother: 1.79 cms. (b) Mother to Female Child: 1.95 cms.

34. 34 Limitation 1. Data collection is done by distributing questionnaire (Anthropometrical measurements on height are not taken). 2. Sample size (a) From Questionnaire Male: 136Female: 55 (b) From Matrimonial website www.shaadi.com Male: 840Female: 840 3. Due to less data from matrimonial website www.shaadi.com (of 21 years), we are unable to detect cyclic variation in Time Series Analysis.

35. 35 Suggestions 1. 1. Prediction can be better if sample size is increased along with increase in no. of generations. 2. If data on tallest persons are collected, better prediction can be made for the tallest person in future.

36. 36 Questionnaire Candidate Name: - Gender: - State: - Height (In Cms.): - Father’s Height (In Cms.): - Mother’s Height (In Cms.): - Grand-Father’s Height (In Cms.): - Grand-Mother’s Height (In Cms.): -

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