Recently, Adam put larger wheels on his skateboard and noticed it would coast farther. He decided to test this relationship. He collected some skateboards, attached wheels of various sizes to them, and rolled them to see how far they would roll on their own. He collected the data shown in the table.
Wheel diameter (in.) x Rolling distance (in.) y
1 ........................................ 17
2 ........................................ 23
3.5 ...................................... 32
5 ........................................ 30
5.5 ...................................... 36
7 ........................................ 52
8.5 ...................................... 57
9.5 ...................................... 55
10 ...................................... 70
a. Make a scatter plot of these data.
b. Does there appear to be a linear relationship between the variables? Find the correlation coefficient, and use this value to justify your answer.
c. Find the equation of the least squares line that models these data.
d. Describe the real-world meaning of the slope and the y-intercept of your line.
e. Use your model to determine the size of wheel of a skateboard that rolls 50.5 in.