Final answer:
An explanatory variable is an independent variable that researchers manipulate in an experiment to see its effect on a dependent variable. In a graph, this is usually represented as variable X on the horizontal axis. The goal in experiments is to isolate this variable to measure its impact accurately on the response variable, which is depicted as Y on the vertical axis.
Step-by-step explanation:
An explanatory variable is a type of independent variable that is manipulated in an experiment to determine its effect on a dependent variable, often denoted as the response variable. In mathematical terms, consider the scenario where we're analyzing data points on a graph with two axes. Here, if we take variables X and Y, typically X would be the explanatory variable on the horizontal axis, and Y would be the response variable on the vertical axis.
For example, consider the linear equation y = mx + b which describes a straight line on a two-dimensional plot with x as the explanatory variable and y as the response variable. When graphing data, the variable on the horizontal x-axis is the one that we change or control to see its effect on the variable on the vertical y-axis. Factors m and b determine the slope and intercept of the line respectively.
To understand the relationship between variables, it is essential to isolate the explanatory variable in an experiment. This can be done through random assignment of subjects to control for lurking variables that might otherwise cloud the results. When conducting an experiment, we aim to compare groups that only differ in the treatments they receive.
In practical terms, if we're looking at how study time influences test scores among students, study time would be our explanatory variable (X) and test scores would be our response variable (Y). If X is increased, we'd observe the effects on Y to understand the relationship between study time and test score success.