We use the form
ŷ = a + bx
for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept.
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 0.8597 0.4148 2.07 0.1069
Weight 0.41132 0.02978 13.81 0.0002
S = 0.517508, R-Sq = 97.9%
Notice that "Weight " is listed under "Predictor." This means that weight is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation
ŷ = a + bx.
(a)
Write out the least-squares equation. (Let x be the weight of a child in kilograms.)
ŷ =

(b)
For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Enter your answer to five decimal places.)
(c)
What is the value of the correlation coefficient r? (Round your answer to four decimal places.)
r =
(d)
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?
%