Question

The table below shows the velocity y, in miles per minute, of a toy car at different times x, in minutes: Time (x) (minutes) 10 20 30 40 Velocity (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 velocity 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 velocity 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?

Answer 1

A. If you plot the points in a graph, it would look like that shown in the picture attached. If we use linear regression, the correlation is very poor. The coefficient of correlation (r2) is only 0.0017. There is no linear relationship between time and velocity.

B. The slope of the graph is equal to y2-y1/x2-x1, In this case, it would specifically be v2-v1/t2-t1

Slope = 0.8-0.2/20-10 = 0.06 miles/s^2

The slope represents the acceleration at time 10 to 20 minutes.

C. The table in the graph shows causation rather than correlation. The points in the data occur in a sequential manner.