Question

The table below shows the distance y, in miles per minute, of a toy car at different times x, in minutes: Time (x) (minutes) 10 20 30 40 Distance (y) (miles) 0.2 0.8 0.1 0.4 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 of the toy car. (4 points) [Choose the value of correlation coefficient from −1, 1, −0.04, 0.99] Part B: What is the value of the slope of the graph of distance versus time between 10 minutes and 20 minutes, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)

Answer 1

Part A: the correlation coefficient is −0.0417 or −0.04. This means that there is a negative correlation; as one variable increases, the other decreases. Since the coefficient is close to zero, the variables are said to have no linear relationship or have a very weak linear relationship.

Part B: the slope is 0.06. This represents the change of distance per time or miles per minutes of the toy car.
m = y2 - y1 over x2 - x1
m = 0.8 - 0.2 over 20 - 10
m = 0.6 / 10
m = 0.06

Part C: the data represent correlation. Correlation is a statistical measure (expressed as a number) that describes the size and direction of a relationship between two or more variables. Since the two data is more of a relationship between each other than the cause and effect of each other. It's not causation because the increase in time does not necessarily cause the increase or decrease in miles or vice versa.