[Statistics] Independent vs. Dependent Variables

[statisticsquestion]

Hi everyone I have a quick question about independent and dependent variables.

Homework Statement

The following data set gives the number of miles traveled, and the travel time in hours for each of the 10 car's driving assignments.

Miles Time
90 9
40 5
90 9
90 6
45 4
75 6
60 7
63 6
85 7
85 6

PART A.
Use regression analysis to determine the independent variable and the dependent variable.

PART E.
Assuming that 75 miles are traveled by a car, use your model to predict the travel time.

The Attempt at a Solution

I said that the independent variable was time and the dependent variable was miles traveled. My solution was marked incorrect. Here is my justification:

"I was under the impression that distance is always a function of time traveled and therefore travel time ought to be the independent variable because the distance depends on changes in time.
In physics and mathematics, velocity and acceleration are 1st and 2nd derivatives of displacement respectively. This is so because they depend on displacement (distance traveled) with respect to time."

Grader's response:
"The dependent variable is the variable that we are trying to predict. So it varies based on the scenario and the problem that needs to be solved. In this case we need to predict travel time (see part e). Hence travel time in this scenario is the dependent variable."

My confusion
I feel like the question could have been elaborated better (explicitly stating which variable was under direct control). Nevertheless, it doesn't make sense to me how I would have to look at the question in part E to determine how to move forward for part A.

Can someone please further elucidate why time is not the independent variable in this instance?

Thanks.

 

[drvrm]

Use regression analysis to determine the independent variable and the dependent variable.

In simple linear regression, the model used to describe the relationship between a single dependent variable Sat time t as y and a single independent variable say distance traveled as x is
y = a0+ a1x + k.
a0 and a1 are referred to as the model parameters, and k is a probabilistic error term that accounts for the variability in y that cannot be explained by the linear relationship with x.
If the error term were not present, the model would be deterministic; in that case, knowledge of the value of x would be sufficient to determine the value of y.
alternatively a scatter graph of distance and time can be drawn and a mean linar graph can be used for prediction.
Regarding the grader's argument ... i can say that they wanted to predict the time taken , so the dependent variable can be taken to be 'time'.

 

[billy_joule]

My confusion
I feel like the question could have been elaborated better (explicitly stating which variable was under direct control). Nevertheless, it doesn't make sense to me how I would have to look at the question in part E to determine how to move forward for part A.

Can someone please further elucidate why time is not the independent variable in this instance?

A "driving assignment" is some given destination ie drive to bobs business on main street.
The time required to get to that location is dependant on how far away that location is.

A "driving assignment" is not - drive for X hours and let's see how far you get. (unless you consider le Mans 24hr race a driving assignment..)
I think it's fairly reasonable to expect students to determine this via common sense.

However, the question is poor and so is the graders response. Regression analysis cannot determine the dependant and independent variable in this case.
If you are a delivery driver, time is dependant, if you're a Le Mans driver, distance is dependant, regression cannot determine what type of driver the data comes from.
All regression can say is that driving for more time results in greater distance traveled and vice versa.

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