Final answer:
The correct statement about the Pearson correlation coefficient (r) is that r is higher when the data is continuous, there's a linear relationship, and homoscedasticity is present. Values near -1 or +1 indicate strong linear relationships, whereas values close to 0 depict weak or no linear relationship.
Step-by-step explanation:
The correct statement regarding the Pearson correlation coefficients (r) is the first one: r is higher when the necessary assumptions (continuous data, linear relationship, homoscedasticity) are met. This is because the Pearson correlation coefficient is designed to measure the strength and direction of a linear relationship under these conditions.
If r is closer to zero, it indicates a weaker relationship, not a stronger one. Moreover, the Pearson correlation coefficient is used to represent the relationship between two continuous variables, rather than between categorical and numeric variables.
The value of r ranges from -1 to +1, where values close to -1 or +1 indicate a strong linear relationship, while an r value close to 0 suggests no linear relationship. Correlation coefficient of 0.9 implies a much stronger linear relationship than an r of 0.3, for example.
A positive correlation is indicated by a positive r value, meaning that as one variable increases, the other tends to increase as well. Conversely, a negative correlation is shown by a negative r value, which means that as one variable increases, the other tends to decrease.