- #1

## 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.