Question

Underinflated or overinflated tires can increase tire wear and decrease gas mileage. A manufacturer of a new tire tested the tire for wear at different pressures. Construct scatterplot and calculate Pearson correlation coefficient. The researcher for this study calculated a Pearson correlation coefficient and concluded no relationship existed between the two variables. Was he correct in his conclusion?

Pressure	Mileage(thous)
30	29.5
30	30.2
31	32.1
31	34.5
32	36.3
32	35
33	38.2
33	37.6
34	37.7
34	36.1
35	33.6
35	34.2
36	26.8
36	27.4

Answer 1

Above is the scatterplot of the data.

The person correlation coefficient = -0.1137.

Pearson correlation coefficient only measures the srength of linear relationship. The linear relationship between variables is almost non-existent as the pearson correlation coefficient is close to 0. However, from the scatterplot, we can see that there is still some relationship between the 2 variables which is non-linear or rather circular in nature. Hence, the researcher is wrong.