Question

The accompanying data on x = head circumference z score (a comparison score with peers of the same age - a positive score suggests a larger size than for peers) at age 6 to 14 months and y = volume of cerebral grey matter (in ml) at age 2 to 5 years were read from a graph in an article. Head Circumfer- Cerebral Grey Matter (ml) 2-5 yr encez Scores at 6-14 Months 680 -0.74 690 1.8 700 -0.29 720 0.26 740 0.31 740 2.1 750 1.7 750 2.6 760 1.7 780 1.7 790 2.6 810 2.7 815 820 825 3.4 2.8 0.91 2.95 835 2.9 840 845 2.8 (a) What is the value of the correlation coefficient? (Give the answer to two decimal places.) (b) Find the equation of the least-squares line. (Give the answer to two decimal places.) (c) Predict the volume of cerebral grey matter for a child whose head circumference z score at age 12 months was 1.7. (Give the answer to two decimal places.)

Answer 1

A B C D E F 1 SR NO Y X Y^2 X^2 XY 1 2 3 4 2 3 4 -503.2) 1242) -203 187.2) 229.4 5 5 6 6 7 8 9 10 7 81 9 10 680 690 700 720 740 740 750 750 760 780 790 810 815 820 825 835 840 845 -0.74 1.8 -0.29 0.26 0.31 2.1 1.7 2.6 1.7 17 2.6 2.7 3.4. 2.8 0.91 2.95 2.9 2.8 4624001 476100 490000 518400 547600 547600 562500 562500 577600 608400 624100 656100 664225 672400 680625 697225 705600 714025 0.5476 3.24 0.0841 0.0676 0.0961 4.41 2.89 6.76 2.89 2.89 6.76 7.29 11.56 7.84 0.8281 8.7025 8.41 7.84 11 12 13 14 15 11 12 13 14 15 16 17 18 1554) 12751 1950 1292 1326 2054 2187 27711 2296 750.751 2463.25 2436 2366 16 17 18 19 20 SUM 13890 32.2 10767400 83.106 25673.41 21 22

857 a) r= Sxy Vsax: Syy where Sxy = Exy - ElEy) 70 Sua= [x² - (2x)2/n syy = {.y? (sy)? In here n=18 219 - 256734) Ex= 32.2, Zy=43890 Zx²= 81.106 Ey? =10767400 = .. Sxy = 25673.4 - (32:2 x 13890)/18 = 8251 7333 Sxx=81.106 (32.2)²/18 25.50.38 = 10767400.- (13890)/18 = 4.89 50 Syy 0.739028 825.7333 25.50388 48950 :r=0.74 b) equation of least square line is ŷ = at bx where a = ý - b & b = say sax b = 825-7333 = 32. 3769 = 32.38 25.5038

a= TG - b. { 13890 32.37698 32.2 18 18 ē 713.74799 = 713-75 Y = 713.75 + 32:38% c) when x=1-7 ŷ =713.75+ 32-38 x1,7 = 768.796 = 7.68.8 :. Predicted valueme of cerebral gray matter for a child whose head circumference 2-score at age 12 months was 1.7 is 768.8

a= TG - b. { 13890 32.37698 32.2 18 18 ē 713.74799 = 713-75 Y = 713.75 + 32:38% c) when x=1-7 ŷ =713.75+ 32-38 x1,7 = 768.796 = 7.68.8 :. Predicted valueme of cerebral gray matter for a child whose head circumference 2-score at age 12 months was 1.7 is 768.8