Question

a pediatrician wants to determine the relation that may exist between a childs height and head circumference. she randomly selects 8 children, measures their height and head circumference, and obtains the data shown in the table.
(a) if the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable and which is the response variable.
the explanatory variable is head circumference and the response variable is height.
the explanatory variable is height and the response variable is head circumference.
(b) draw a scatter diagram. which of the following represents the data?

Explanation:

• Part (a):
• In regression analysis, the explanatory variable (\(x\)) is used to predict the response variable (\(y\)). Here, height is used to predict head circumference. So, height is the explanatory variable (\(x\)) and head circumference is the response variable (\(y\)).
• Part (b):
• For a scatter - diagram, the \(x\) - axis represents the explanatory variable (height) and the \(y\) - axis represents the response variable (head circumference).
• Looking at the options:
• Option A has height on the \(x\) - axis and head circumference on the \(y\) - axis which is consistent with the roles of explanatory and response variables (height (\(x\)) to predict head circumference (\(y\))).
• Option B has head circumference (\(x\)) and height (\(y\)) which is the reverse of what we need.
• Option C has incorrect axis labels (e.g., height on \(y\) - axis and wrong range for \(y\) - axis values).
• Option D has incorrect axis labels (e.g., head circumference on \(x\) - axis and wrong range for \(y\) - axis values).

Answer:

• (a) The explanatory variable is height and the response variable is head circumference.
• (b) A.