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 females.

x (lb)	21	23	22	24	20	15	25	21	17	24	26	22	18	19
y (lb)	124	122	121	123	130	120	145	130	130	130	130	140	110	115

In this setting we have Σx = 297, Σy = 1770, Σx² = 6431, Σy² = 224,880, and Σxy = 37,734.

(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

(b) Find 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.)

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

t =

Find the p value =

(d) If a female baby weighs 15 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.)

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

(f) Find a 95% confidence interval for weight at age 30 of a female who weighed 15 pounds at 1 year of age. (Round your answers to two decimal places.)

lower limit	______ lb
upper limit	______lb

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

t =

Find the P value =

(h) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)

lower limit ______
upper limit ______

Answer 1