Which of the following methods provides a “relationship” between two variables?

To analyze the relationship between two variables, various methods can be considered. Some of the common methods include:

1. Correlation: This statistical measure expresses the extent to which two variables are linearly related. The correlation coefficient, usually denoted as $r$, ranges from -1 to +1, where values close to +1 indicate a strong positive relationship, values close to -1 indicate a strong negative relationship, and a value of 0 indicates no relationship.

2. Regression Analysis: This method involves fitting a line or curve to the data points, which helps in quantifying the relationship between the independent variable (predictor) and the dependent variable (outcome). Simple linear regression is the most basic form, modeled by the equation $Y = a + bX$, where $Y$ is the dependent variable, $a$ is the intercept, $b$ is the slope, and $X$ is the independent variable.

3. Scatter Plots: This graphical representation can help visualize the possible relationship between two numeric variables. The pattern of the points can show whether a relationship exists.

4. Chi-Squared Test: For categorical data, this test examines the association between two nominal variables.

In summary, methods such as correlation and regression analysis directly provide a mathematical or statistical relationship between two variables, while scatter plots help visualize that relationship.