Final answer:
In a deterministic relationship, the response variable is uniquely determined by the values of the predictor variables. Among the choices, the correct answer is B. Deterministic. Linear regression is a statistical tool that can analyze such relationships, using the correlation coefficient and the coefficient of determination to quantify the strength and significance of the relationship.
Step-by-step explanation:
If the value of the response variable is uniquely determined by the values of the predictor variables, we say that the relationship between the variables is deterministic. A deterministic relationship means that there is a direct, predictable connection between the variables; if you have the predictor variable, you can accurately predict the response variable.
In the context provided:
- A regressive relationship would imply going backwards or declining, which is not relevant here.
- A random relationship would imply there is no predictable association between variables.
- A stochastic relationship would imply some level of randomness in the connection between predictor and response variables, even if a general trend exists.
Given the choices, the correct answer is B. Deterministic.
Regression analysis, and specifically linear regression, is the tool often used to explore the relationship between a dependent variable and one or more independent variables. This could be done using a simple linear model (e.g., y = a + bx), which is useful when the relationship looks to be a straight line on a scatter plot, indicating a possible linear relationship. The coefficient of determination, r², derived from the correlation coefficient (r), provides insight into how much variance in the response variable can be explained by the predictor.