Question

1. Lutein is an important carotenoid in the maintenance of ocular health. The study began in 1999 to measure the lutein and the lutein was re-measured in 2003.

	1999 Serum-lutein value (ug/dL)	2003 Serum-lutein value (ug/dL)
1	3.5	6.4
2	2.9	7.5
3	4.1	8.4
4	5.1	9.6
5	6.4	12
6	1.9	4.2
7	1.3	3.1
8	4.1	6.3
9	2.3	4.4
mean	3.511	6.878
sd	1.616	2.839

1) Calculate the Pearson correlation coefficient using the formula learned at class and test if there is a significant different from 0.

2) Using regression method, derive a calibration formula predicting the 2003 value as the function of the 1999 value.

3) Suppose a participant had a 1999 serum-lutein value of 5.0 ug/dL. What is that person’s serum lutein based on 2003 assay?

Answer 1

1994 X4 3.5 2003 6.4 | 3-5x6.4 -22.4 x = 3.5।। 9 26.878 F- 1616 2.१ ५.) 7.5 1.15 | 34.44 5.। 48.96 y - २.839 १.6 12 प - ७० 16.8 7.8 .१ 4.2 1.3 3. 4.03 4.) 25083 6.3 4.4 2.3 10. 12 ६xy -25२.3) Covcx, 4) - | 2x4-- -/JX852 -37) - (3.511-6.878) : 28.0344 - २५.1487 3.885

peallon correlation coefficient 4 COVCX, 4) 3. 8857 (1.616 x 2.839) 3.8857 4.5878 = 0.8470 r. 0-847. Null hypothesis Ho: PO Alternatwe hypothesis H P D . e n -9, def-n-2 = 9-2 = 7 Gutical realue for 7 d f at u=0.05 is to. 666 r=0.847 0.666. So s'is significant at x = 0.05 we reject to (2) you x The regression equation 4-ý = roy (x-x) is (y - 6.878) = 084 x 2.83 3.51) 1.616

ya 6.878 - 1.488 / x - 3.511) 4-6878 - 1.488 X - 5.224. 'Y - 60878 +5.224 = 1488x y = 1.4882 + 1.654. x=5.0 ug/dL yo 2 + = 1 + 488 (5, 0) + |- 654 Y = 7.44 +10654 $ - 9 094. The person's serum lutein based 2003 assay is 90094 uglde on