Which of the following are properties of the linear corielation coefficient? Select all that apply. \( \square \) If \( \mathrm{r}=-1 \), then a perfect negative linear relation exists between the two variables. \( \square \) A linear correlation of -0.742 suggests a stronger negative association between two variables then a linear correlation of - 0.472 . \( \square \) If \( r \) is close to 0 , then little or no evidence of any relation belween the explanatory or response variable exists. \( \square \) The lorrelation coelticient is resislant. \( \square \) Thear correlation coefficient is always between -1 and 1 . That is, \( -1 \leq \mathrm{r} \leq 1 \).

Let's evaluate each statement regarding the properties of the linear correlation coefficient: 1. **If \( \mathrm{r}=-1 \), then a perfect negative linear relation exists between the two variables.** - **True**: A correlation coefficient of -1 indicates a perfect negative linear relationship. 2. **A linear correlation of -0.742 suggests a stronger negative association between two variables than a linear correlation of -0.472.** - **True**: The absolute value of -0.742 is greater than that of -0.472, indicating a stronger negative correlation. 3. **If \( r \) is close to 0, then little or no evidence of any relation between the explanatory or response variable exists.** - **True**: A correlation coefficient close to 0 suggests that there is little to no linear relationship between the variables. 4. **The correlation coefficient is resistant.** - **False**: The correlation coefficient is not resistant; it can be heavily influenced by outliers. 5. **The correlation coefficient is always between -1 and 1. That is, \( -1 \leq \mathrm{r} \leq 1 \).** - **True**: The correlation coefficient is indeed bounded between -1 and 1. Based on this evaluation, the correct properties of the linear correlation coefficient are: - \( \square \) If \( \mathrm{r}=-1 \), then a perfect negative linear relation exists between the two variables. (True) - \( \square \) A linear correlation of -0.742 suggests a stronger negative association between two variables than a linear correlation of -0.472. (True) - \( \square \) If \( r \) is close to 0, then little or no evidence of any relation between the explanatory or response variable exists. (True) - \( \square \) The correlation coefficient is resistant. (False) - \( \square \) The correlation coefficient is always between -1 and 1. That is, \( -1 \leq \mathrm{r} \leq 1 \). (True) So, the true statements are the first, second, third, and fifth.