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 ­les produced the following information for 14 females:

Σx = 300; Σy = 1775; Σx² = 6572; Σy² = 226,125; Σxy = 38,220

(a) Draw a scatter diagram for the data.

(b) Find x, y, b, and the equation of the least-squares line. Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coef­ficient r and the coef­ficient of determination. What percentage of the variation in y is explained by the least squares model?

(d) Test the claim that the population correlation coef­ficient r is positive at the 1% level of signifi­cance.

(e) If a female baby weighs 20 pounds at 1 year, what do you predict she will weigh at 30 years of age?

(f) Verify that S_e ≈ 8.38.

(g) Find a 95% con­fidence interval for weight at age 30 of a female who weighed 20 pounds at 1 year of age.

(h) Test the claim that the slope b of the population least-squares line is positive at the 1% level of signi­ficance.

(i) Find an 80% con­fidence interval for b and interpret its meaning.

Transcribed Image Text:

x (Ib) 21 25 23 24 20 5 25 21 17 24 26 2218 19 y (lb) 125 125 120 125 130 120 145 130 130 130 130 140 110 115