Question

what are the independent and dependent variables represented by the investigative question?
you ask an automobile insurance policy holder: \what is your age, and what is your annual car insurance premium?\
the independent variable is the
the dependent variable is the
age of the person
insurance premium

Explanation:

To determine independent and dependent variables, we analyze the relationship: Age is a variable that we might think influences car insurance premiums (premiums often vary with age). The independent variable is the one that is manipulated or is the cause, and the dependent variable is the effect (depends on the independent variable). So age is independent (it's the input/cause), and insurance premium is dependent (depends on age).

For the first blank (independent variable): "age of the person" because we consider age as the variable that could explain or cause changes in the other variable.

For the second part (reason for independent): The variable "age of the person" is independent as it is not dependent on the insurance premium (it's a characteristic we measure to see its effect on premium).

For the dependent variable: "insurance premium" because the variable "insurance premium" depends on the age of the person (premiums are set based on factors like age, so age influences premium).

Answer:

The independent variable is the $\boldsymbol{\text{age of the person}}$ because the variable $\boldsymbol{\text{age of the person}}$ (is the explanatory variable, not dependent on premium). The dependent variable is the $\boldsymbol{\text{insurance premium}}$ because the variable $\boldsymbol{\text{insurance premium}}$ (depends on the age of the person).