Question

Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year-old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 female subjects: X(lb)| 21 25 23 24 20 15 25 21 17 24 26 22 18 19 y (lb) 125 125 120 125 130 120 145 130 130 130 130 140 110 115 8.38. 2x-300; Zy-1,775; ΣΧ2-6,572 ; Σy2-226,125; Σχy : 38,220; and Se Drag blue round points onto the following graph tool to draw a scatter diagram for the data. Weight of mature adult (lb 150 145 140 135 130 125 120 115 110 105 100 14 16 18 20 22 24 2628 Weight of 1 yr old baby (lb) Clear All Find R, 9, a, and b, and complete the equation of the least-squares line. Round your answers to three decimal places.) Find the sample correlation coefficient r and the coefficient of determination. Round your answers to three decimal places.) What percentage of the variation in y is explained by the least-squares model? The percentage of variation in y that is explained by the least-squares model is If a female baby weighs 20 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) Prediction for weight at 30 years of age, y - Do you expect this prediction to be useful? pounds O Yes O No

Answer 1

YValues

36388416739114 7 )-736556 .3226 7 06044361484 58 71428517228518 653229659 258118258 1746037166 .37 0226212096201 77773733333377 55554544444455 11613683333361 27772272277722 45554454455544 03121630424032

Sum of X = 300
Sum of Y = 1775
Mean X = 21.4286
Mean Y = 126.7857
Sum of squares (SS_X) = 143.4286
Sum of products (SP) = 184.2857

Regression Equation = ŷ = bX + a

b = SP/SS_X = 184.29/143.43 = 1.285

a = M_Y - bM_X = 126.79 - (1.28*21.43) = 99.253

ŷ = 1.285X + 99.253

58322 73655603226556 06044351484778 1 2 1 1 52 2 2 2 1387333367 33630610000418 8 12-0 228758 371668378 262-2⑤960015 2 2 3 77772722222277 11613683333361 6 99199 2 2 45554454455544 4 03121630424032 1

X Values
∑ = 300
Mean = 21.429
∑(X - M_x)² = SS_x = 143.429

Y Values
∑ = 1775
Mean = 126.786
∑(Y - M_y)² = SS_y = 1080.357

X and Y Combined
N = 14
∑(X - M_x)(Y - M_y) = 184.286

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 184.286 / √((143.429)(1080.357)) = 0.468

r^2=0.219

So explained variation is 21.9%