Question

The table below shows the distance y, in miles, traveled by a toy car in x minutes:

time in x minutes| 20 |30 |40 |50
Distance in x miles|5|10|15|20

Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and distance traveled by the toy car. (4 points)

Answer 1

First, plot the points.
(20, 5), (30, 10), (40, 15), (50, 20)

A. You'll see that it's a perfectly straight line, so it's a perfect positive correlation --- Positive because it increases from left to right. The value to represent this is 1. A correlation of 1 means time and distance have a perfect positive linear relationship, meaning if x increases by a certain value, y also increases by a certain value at the same time. In our case, every time x increases by 10, y increases by 5
The slope represents the rate (or speed). Distance, rate, and time are related by

             distance = rate • time
distance / time = rate
            rise / run = m
                       1/2 = m
It's a correlation because x and y are related by a common pattern
The car's speed is 1/2 miles per minute.