Which statement about correlation is true?

Which statement about correlation is true?

• A. Correlation cannot exist without causation
• B. This summary statistics regression tends to yield a lower correlation
• C. Regression based on summary statistics can yield a higher correlation
• D. Correlation values range only between 0 and 1

Answer: (C)

The assertion that regression based on summary statistics can yield a higher correlation is accurate. Correlation is a measure of the strength and direction of the linear relationship between two quantitative variables, and it is represented by the correlation coefficient, which ranges from -1 to 1. When summary statistics are used, such as means and standard deviations, to calculate the correlation from a dataset, it can reflect the strength of the linear relationship even if the individual data points exhibit variability. If the underlying relationship between the two variables is strong and linear, the correlation calculated from summary statistics can indeed appear higher than any correlation derived from a smaller, less representative sample of data points. This highlights the significance of considering the entire dataset when evaluating relationships between variables. In contrast, the other options misrepresent fundamental concepts in statistics. Correlation does not imply causation, so correlation can exist without a causal relationship between the variables. The range of correlation values is from -1 to +1, not just between 0 and 1, thus including negative correlations which indicate an inverse relationship. Furthermore, when discussing summary statistics and regression, they might not inherently yield lower correlation; it varies based on data characteristics and the approach used for analysis.

The assertion that regression based on summary statistics can yield a higher correlation is accurate. Correlation is a measure of the strength and direction of the linear relationship between two quantitative variables, and it is represented by the correlation coefficient, which ranges from -1 to 1.

When summary statistics are used, such as means and standard deviations, to calculate the correlation from a dataset, it can reflect the strength of the linear relationship even if the individual data points exhibit variability. If the underlying relationship between the two variables is strong and linear, the correlation calculated from summary statistics can indeed appear higher than any correlation derived from a smaller, less representative sample of data points. This highlights the significance of considering the entire dataset when evaluating relationships between variables.

In contrast, the other options misrepresent fundamental concepts in statistics. Correlation does not imply causation, so correlation can exist without a causal relationship between the variables. The range of correlation values is from -1 to +1, not just between 0 and 1, thus including negative correlations which indicate an inverse relationship. Furthermore, when discussing summary statistics and regression, they might not inherently yield lower correlation; it varies based on data characteristics and the approach used for analysis.