Question

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). Predictor Coef SE Coef T P Constant 0.8489 0.4148 2.06 0.84 Weight 0.39161 0.02978 13.52 0.000 S = 0.517508 R-Sq = 94.6% (a) Write out the least-squares equation. y hat = + x (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.) (c) What is the value of the correlation coefficient r? (Use 3 decimal places.)

Answer 1

Answer:

Let

x = body weight of the child

y = metabolic rate of the child

(a) Write out the least-squares equation

ŷ = 0.8489 + 0.39161 x

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

For each 1 kilogram increase in weight, metabolic rate of a child is expected ro increase by 0.39161

(c) We have to find  the value of the correlation coefficient r:

Here

R-Sq = 94.6%

R-Sq = 94.6/100

R-Sq = 0.946

correlation coefficient r = √(0.946)

correlation coefficient r = 0.973

Therefore the value of the correlation coefficient r is 0.973