Question

car rideshare services are a popular option for people needing to move about in large cities. the scatterplot shows the distances 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.

Explanation:

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. It is not affected by which variable is plotted on the \(x\)-axis and which is plotted on the \(y\)-axis. The formula for the correlation coefficient \(r=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2\sum_{i = 1}^{n}(y_i-\bar{y})^2}}\). Swapping \(x\) and \(y\) in the formula does not change the value of \(r\).

Answer:

The value of the correlation coefficient would not change.