In each of the four examples listed below, one of the given variables is independent (x) and one of the given variables is dependent (y). Indicate in each case which variable is independent and which variable is dependent.

I. Gas consumption; Miles driven
II. Course grade; Test score
III. Ability to concentrate; Level of fatigue
IV. Size of package; Cost to ship

y,x

y,x
y,x
x,y

Thank You!!

To determine which variable is independent and which variable is dependent in each case, you need to understand the concept of independent and dependent variables.

In an experiment or study, an independent variable is the one that is deliberately manipulated or controlled by the researcher. It is the variable that is believed to cause a change or influence the outcome of the dependent variable. On the other hand, a dependent variable is the outcome or response that is being measured or observed. It is the variable that is expected to be affected by changes in the independent variable.

Let's analyze each example:

I. Gas consumption; Miles driven
In this case, the independent variable is "Miles driven." This is because the amount of gas consumed depends on the distance traveled. As you drive more miles, the gas consumption increases. Therefore, "Gas consumption" is the dependent variable.

II. Course grade; Test score
The independent variable here is "Test score." The grade in a course is determined by the scores achieved on different tests. The course grade is dependent on the individual test scores. Hence, "Course grade" is the dependent variable.

III. Ability to concentrate; Level of fatigue
Here, the independent variable is "Level of fatigue." The ability to concentrate may vary depending on how tired or fatigued a person is. The level of fatigue influences the ability to concentrate. Therefore, "Ability to concentrate" is the dependent variable.

IV. Size of package; Cost to ship
In this case, the independent variable is "Size of package." The cost to ship a package is generally determined by its size. Larger packages require more resources and space, resulting in a higher shipping cost. Thus, "Cost to ship" is the dependent variable.

Remember that in each of these examples, the independent variable is the one that causes or influences the changes in the dependent variable.