The following equation can be used to predict the average height of boys anywhere between birth and 15
years old: y = 2.79x +25.64 where x is the age (in years) and y is the height (in inches).
a. What does the slope represent in this problem? Interpret it in context.
b. What does the y-intercept represent in this problem? Interpret it in context.
Slope is age?
a. In this equation, the slope represents the rate of change of height with respect to age. Specifically, the slope value of 2.79 means that for every increase of one year in age, the average height of boys is expected to increase by 2.79 inches.
In context, this means that as boys get older, they tend to get taller at a relatively constant rate of 2.79 inches per year. This relationship suggests a positive correlation between age and height, where older boys are generally taller than younger boys.
b. The y-intercept in this equation represents the height at the starting point, when the age is zero. In context, the y-intercept value of 25.64 inches means that at birth (when age is zero), the average height of boys is expected to be 25.64 inches.
However, it is important to note that since age cannot be negative, the y-intercept is not a meaningful data point in the context of this problem. It is simply a result of the mathematical equation and should not be interpreted as representing an actual height at birth.