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 females.x (lb)1924252320152521172426221819y (lb)126126125124130120145130130130130140110115In this setting we have Σx = 298, Σy = 1781, Σx2 = 6492, Σy2 = 227,603, and Σxy = 38,105.(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your answers for least-squares estimates to four decimal places.)x= y= b= ŷ= + xind the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) %(d) Test the claim that the population correlation coefficient ? is positive at the 1% level of significance. (Round your test statistic to three decimal places.)t = If a female baby weighs 21 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) lb(f) Find Se. (Round your answer to two decimal places.)Se = (g) Find a 95% confidence interval for weight at age 30 of a female who weighed 21 pounds at 1 year of age. (Round your answers to two decimal places.)lower limit lbupper limit lb(h) Test the claim that the slope ? of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.)t =

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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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 females.

x (lb)	19	24	25	23	20	15	25	21	17	24	26	22	18	19
y (lb)	126	126	125	124	130	120	145	130	130	130	130	140	110	115

In this setting we have Σx = 298, Σy = 1781, Σx² = 6492, Σy² = 227,603, and Σxy = 38,105.

(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your answers for least-squares estimates to four decimal places.)

x	=
y	=
b	=
ŷ	=	+ x

ind the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

r =
r² =

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
%

(d) Test the claim that the population correlation coefficient ? is positive at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

If a female baby weighs 21 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.)
lb

(f) Find S_e. (Round your answer to two decimal places.)
S_e =

(g) Find a 95% confidence interval for weight at age 30 of a female who weighed 21 pounds at 1 year of age. (Round your answers to two decimal places.)

lower limit	lb
upper limit	lb

(h) Test the claim that the slope ? of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

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