Question

Regression 1 You are interested in an association between age and gum recession (measured as the average over all surfaces for a patient) You measured data from 5 patients Age (years) Recession (mm)( - }* (y _ ¥)* (x-(y-g) 3 0.8 400 1.44 24 1.2 225 0.64 12 20 2.2 0.04 -0.6 27 1.9 16 0.01 -0.4 64.6 57 3.9 1156 3.61 Note that the average age is 23 years and average gum recession is 2. You want to see if there is a linear relationship between age and gum recession This is a long problem so please show your work so I can find mistakes and award partial credit. a. What is SS? b. What is SSy? c. What is SSr (also known as SSy)? d. What is the slope of the regression line? e. It has been 10 years since you last saw a patient, how much would you predict their recession to have increased? f. What is the intercept of the regression line?

Answer 1

The provided Solution: in tbemaths in the question Age Associatin between age m recession measured data tom s patients a Age gears) Recession (mm) of 50) 2 - 0.8 900 8 1.2 225 20 2 2. 7 27 lig 16 57 3g 1156 Exi=115 211=10 Z (2; -7) K-23 1=2 = 1806 cyng) (sese) (49) 1.44 24 0.64 12 0.04 -0.6 0.01 -0.4 361 64.6 214-9²= [(x-7)(y-7)= sotu 299.6 Here n =5 a) What T s Sort - 1 ssex S (x-7) 2 SSxx = 1 x 1806-361.2 Sxx = 361.2 Ssxy = 1 ZC5) ²09-9) 2 = 4x996 19.93 Issay = 19.92] & What is sor (also known as shey) n ssy = 12 (4-9)² = 4 x 5.74 = 1.148 5 st = 10148

d). Sy lahat B the slope of the regression linge slope A regressin line (y=a+bx) = b b= slope = {(x; -x) 64; -7) Ecxi-x)2 99.6 - 0.05515 Slope - a to have • It has been 10 yeors since you last sato patient, how much predict thelę recession Increased Regaession line Y-0.73 1561 +0.05515 x 4 -0.73 15 61+0.05515 x 10 ya 1. 288656 Ty=103 Hence 113 recession increased. I what is the intercept of regressrohe Regreession line yra tbx. a = Intercept 9- b ų =2-0.05515 X 23 -2-1.2684 -0.73156 Regression time to atbx = 0.737561 +0.05515 x