To determine which type of relationship least-squares regression can be used for predicting between explanatory and response variables, let's consider the options:
a. Linear relationship: Least-squares regression is most commonly used for linear relationships. It fits a line to the data that minimizes the sum of the squared differences between the observed values and the values predicted by the line.
b. Quadratic relationship: This involves fitting a parabola to the data. While least-squares regression can be extended to handle quadratic relationships, it's not its primary use.
c. Cubic relationship: Similar to quadratic relationships, least-squares regression can be adapted to handle cubic relationships by fitting a cubic polynomial to the data. However, this again is an extension rather than the core application of least-squares regression.
d. All of the above: Since least-squares regression can be adapted to fit quadratic, cubic, and other polynomial relationships through polynomial regression, this statement would be inclusive but not entirely specific to the primary application.
Given the primary and most straightforward application of least-squares regression,
the correct option is:
☐ a. linear
