Question

7 from unit 3, lesson 9
an airline company creates a scatter plot showing the relationship between the number of flights an airport offers and the average distance, in miles, travelers must drive to reach the airport. the correlation coefficient of the line of best fit is -0.52.
a. are the number of flights offered and average distance driven to the airport correlated?
explain your reasoning.

b. is it likely or unlikely that one of the variables causes the other to change?
explain your reasoning.

Explanation:

Part a

• A correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables.
• The value of \(r\) ranges from \(- 1\) to \(1\).
• If \(r = 0\), there is no linear correlation. If \(r

eq0\), there is a linear correlation. Here, \(r=-0.52
eq0\).

Part b

• Correlation does not imply causation.
• Just because two variables are correlated (in this case, number of flights and average distance driven) does not mean that one variable causes the change in the other. There could be other confounding variables (e.g., population density around the airport, availability of alternative transportation near the airport) that influence both the number of flights and the average distance travelers drive to reach the airport.

Answer:

a. Yes, they are correlated. The correlation coefficient \(r=-0.52
eq0\), so there is a linear correlation (in this case, a moderate - negative linear correlation) between the number of flights offered and the average distance driven to the airport.
b. Unlikely. Correlation (\(r =- 0.52\) here) only shows a relationship (in this case, a linear relationship), but it does not prove that one variable causes the change in the other variable.