Question

Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight, x, or 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. Please use this data to answer all parts of the question.

x (lbs) 21 25 23 24 20 15 25 21 17 24 26 22 18 19

y (lbs) 125 125 120 125 130 120 145 130 130 130 130 140 110 115

note: For these data, ?̅≈ 21.42, ?? ≈ 3.32, ?̅ ≈ 126.79, ?? ≈ 9.12 1.

a. Find the equation of the least-squares line: ?̂ = ? + ??. Round your results to two decimal places.

b. Compute the coefficient of determination, ? ^2 . What percentage of the variation in ? can be explained by the corresponding variation in ? (be sure to write this statement about weight as a 1-year-old and weight as an adult). What percentage is due to other factors? What does this tell you about how well our model fits the given data?

c. Interpret the slope of your least-squares line in the context of this application (what does the specific numeric value of the slope mean in terms of the relationship between weight as a 1-year-old and weight as an adult?).

Answer 1

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