Gwen: The paired sample data of the age and number of home runs of baseball play

Question

Gwen: The paired sample data of the age and number of home runs of baseball players result in a linear correlation coefficient very close to 0. Conclusion older baseball players tend to hit fewer home runs Describe the error in the stated conclusion. A. A linear correlation coefficient very close to 0 implies that there is a linear correlation but it could be a negative correlation instead of a positive correlation as the conclusion incorrectly suggests. B. A linear correlation coefficient very close to 0 implies that there is a linear correlation between the averages but a correlation between the averages does not imply a correlation between individuals as the conclusion incorrectly suggests. C. Correlation does not imply causality as the conclusion incorrectly suggests. D. With a linear correlation coefficient very close to 0, we should conclude that there is not a linear correlation. so there does not appear to be correlation between age and number of home runs as the conclusion incorrectly suggests

Explanation / Answer

When the value of r is close to zero, generally between -0.1 and +0.1, the variables are said to have no linear relationship or a very weak linear relationship. A positive correlation, when r is greater than 0, signifies that both variables move in the same direction.

therefore Option D is the correct answer: With a linear coefficient very close to 0, we should conclude that there is not a linear correlation, so there does not appear to be a correlation between age and number of home runs as the conclusion incorrectly suggests.

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