If one of the two regression coefficients is negative, then the variables are negatively correlated.

Answer

To determine whether the statement "If one of the two regression coefficients is negative, then the variables are negatively correlated" is true or false, we can follow these steps:

### Step 1: Understand Regression Coefficients
Regression coefficients are values that represent the relationship between independent and dependent variables in regression analysis. There are two regression coefficients: one for predicting the dependent variable from the independent variable (often denoted as \( b_{xy} \)) and another for predicting the independent variable from the dependent variable (denoted as \( b_{yx} \)).

**Hint:** Recall that regression coefficients indicate the direction of the relationship between variables.

### Step 2: Relationship Between Regression Coefficients and Correlation Coefficient
The correlation coefficient (denoted as \( r \)) measures the strength and direction of a linear relationship between two variables. A key property is that the sign of the regression coefficients is the same as the sign of the correlation coefficient. This means if one regression coefficient is negative, the correlation coefficient must also be negative.

**Hint:** Remember that a negative correlation indicates that as one variable increases, the other variable tends to decrease.

### Step 3: Analyze the Statement
The statement claims that if one of the regression coefficients is negative, then the variables are negatively correlated. Since we established that the sign of the regression coefficients aligns with the sign of the correlation coefficient, if one regression coefficient is negative, the correlation coefficient must also be negative.

**Hint:** Think about how the signs of the coefficients relate to the overall relationship between the variables.

### Step 4: Conclusion
Since a negative correlation coefficient indicates a negative relationship between the two variables, the statement is indeed true. Therefore, if one of the two regression coefficients is negative, the variables are negatively correlated.

**Final Answer:** The statement is **True**.