Chapter 4.2, Problem 6P

Critical Thinking: Interpreting Computer Printouts Refer to the description of a computer display for regression described in Problem 5. The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/24 hr). The data are based on information from The Merck Manual (a commonly used reference in medical schools and nursing programs).

Predictor	Coef	SE Coef	T	P
Constant	0.8565	0.4148	2.06	0.084
Weight	0.40248	0.02978	13.52	0.000

s = 0.517508 R-Sq = 96.8%

(a) Write out the least-squares equation.

(b) For each 1-kilogram increase in weight, how much does the metabolic rate of a child increase?

(c) What is the value of the sample correlation coefficient r?

(d) Interpretation What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?

For Problems 7-18, please do the following.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums $\sum x,\sum y,\sum x^2,\sum y^2\text{ and }\sum xy$ and the value of the sample correlation coefficient r.

(c) Find $\bar{x},\bar{y},a,\text{ and }b$. Then find the equation of the least-squares line $\hat{y}=a+bx$.

(d) Graph the least-squares line on your scatter diagram. Be sure to use the point $\bar{x},\bar{y}$ as one of the points on the line.

(e) Interpretation Find the value of the coefficient of determination $r^2$. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?

Answers may vary slightly due to rounding.