A study looking at the correlation between cholesterol level and distance between home and work found a correlation coefficient of -0.13. How much of the variance in cholesterol level is explained by distance?

A study looking at the correlation between cholesterol level and distance between home and work found a correlation coefficient of -0.13. How much of the variance in cholesterol level is explained by distance?

• A. 0.17%.
• B. 0.13%.
• C. 13%.
• D. 1.7%.

Answer: (A)

The correlation coefficient, in this case -0.13, indicates a very weak negative relationship between cholesterol levels and the distance between home and work. To determine how much of the variance in cholesterol level is explained by this relationship, one must square the correlation coefficient. Squaring the value of -0.13 yields 0.0169. To express this as a percentage, you multiply by 100, resulting in 1.69%. This is often rounded to two decimal places, leading to the interpretation that approximately 1.7% of the variance in cholesterol levels can be explained by the distance between home and work. In this context, the correct answer captures the appropriate calculation of the variance explained, showing that a weak correlation still provides some insight into the relationship between the two variables. It’s important to interpret such a low percentage as indicative of only a small portion of the variance being explained, suggesting that other factors likely play a significant role in influencing cholesterol levels.

The correlation coefficient, in this case -0.13, indicates a very weak negative relationship between cholesterol levels and the distance between home and work. To determine how much of the variance in cholesterol level is explained by this relationship, one must square the correlation coefficient.

Squaring the value of -0.13 yields 0.0169. To express this as a percentage, you multiply by 100, resulting in 1.69%. This is often rounded to two decimal places, leading to the interpretation that approximately 1.7% of the variance in cholesterol levels can be explained by the distance between home and work.

In this context, the correct answer captures the appropriate calculation of the variance explained, showing that a weak correlation still provides some insight into the relationship between the two variables. It’s important to interpret such a low percentage as indicative of only a small portion of the variance being explained, suggesting that other factors likely play a significant role in influencing cholesterol levels.