Car rideshare services are a popular option for people needing to move about in large cities. The scatterplot shows the distance
s of trips and fares, in dollars, for an adult living in a city over a period of a month. The value of r for the scatterplot is 0.950. How would the value of the correlation coefficient change if the fares were plotted on the x-axis and distances on the y-axis?
The value of the correlation coefficient would be –0.950.
The value of the correlation coefficient would not change.
The value of the correlation coefficient would be closer to 0.
The value of the correlation coefficient would be closer to 1.
The value of the correlation coefficient would not change.
Step-by-step explanation:
If the relationship between distance of trips and fares in dollars gives a correlation coefficient value of 0.950. This can be interpreted to mean that the relationship between both variables is strong and positive such that an increase in distance leads to corresponding increase in fares of the trip and vice versa. Thus, interchanging the axis upon which the variables are plotted would still tied the same correlation Coefficient value as the correlation coefficient does not depend on the axis upon which the variables are plotted.
Next, set up two equations; One where the value inside the absolute value lines is positive, and another where it is negative, and solve both for the variable:
