In data analysis and statistics, explanatory and response variables are used to describe the relationship between two (or more) variables.

1. Explanatory Variable (Independent Variable)

An explanatory variable is the variable that is manipulated or categorized to determine its impact on another variable. It is often referred to as the independent variable because it is assumed to influence or explain changes in the response variable.

Definition: A variable that is believed to cause or explain changes in the response variable.

Example:
(a) In a study examining the effect of exercise on weight loss, the amount of exercise (e.g., hours per week) is the explanatory variable.
(2) In a classroom study, if you are exploring the relationship between study hours and test scores, the number of study hours is the explanatory variable.

2. Response Variable (Dependent Variable)

A response variable is the variable that changes as a result of alterations in the explanatory variable. It is the dependent variable because its variation depends on the explanatory variable.

Example:
(a) Continuing the above example, weight loss (measured in kilograms) is the response variable because it is expected to be influenced by the amount of exercise.
(b) In the classroom study, test scores are the response variable since they depend on the number of study hours.

Example:

Let us learn this by an example of an agricultural experiment to determine how fertilizer affects crop yield. In an agricultural experiment, scientists or farmers often want to understand the effect of various inputs on crop yield. In this specific example, they are investigating how different amounts of fertilizer affect crop yield. Here’s a detailed breakdown of the scenario:

Explanatory variable: Amount of fertilizer applied (measured in kilograms).
Response variable: Crop yield (measured in tons per hectare).
Objective of the Experiment:The goal is to see if applying varying amounts of fertilizer impacts how much crop is produced (i.e., the yield).

Explanatory Variable: Amount of Fertilizer Applied

The amount of fertilizer is the explanatory variable because it is the factor being manipulated in the experiment.

Measured in kilograms: Fertilizer is typically applied in measured amounts, such as 0 kg, 50 kg, 100 kg, 150 kg, etc. per hectare.

The hypothesis might be that increasing the fertilizer will improve the crop yield up to a certain point.
Fertilizer could contain essential nutrients like nitrogen, phosphorus, and potassium, which plants need for growth. The experiment tests if adding more of these nutrients will result in more crops.

Example Manipulation:

One group of crops receives no fertilizer (control group).
Another group receives 50 kg of fertilizer per hectare.
Another receives 100 kg of fertilizer per hectare, and so on.
By changing the amount of fertilizer, the researcher is intentionally varying this explanatory variable to observe its effect.

Response Variable: Crop Yield

The crop yield is the response variable because it represents the outcome that changes based on the amount of fertilizer applied.
Measured in tons per hectare: Yield is a standard measure of how productive the crops are, often expressed as the weight of the harvested crop per unit area (tons of crop per hectare of land). The yield is expected to increase as fertilizer amounts increase, but only to a point (if over-fertilization occurs, the yield might actually decline due to nutrient imbalance or toxicity).

Example Measurement:
In the group that received no fertilizer, the yield might be 1.5 tons per hectare.
In the group that received 50 kg of fertilizer, the yield might increase to 2.0 tons per hectare.
With 100 kg of fertilizer, the yield might be 2.5 tons per hectare.
With 150 kg of fertilizer, the yield might plateau at 2.6 tons per hectare.
Eventually, if too much fertilizer is applied (e.g., 200 kg per hectare), the yield might decrease again, showing that there’s an optimal level of fertilizer use.

Why is This Important?

Understanding the relationship between the amount of fertilizer (explanatory variable) and crop yield (response variable) helps farmers optimize resource use, avoid wasting fertilizer (which is costly and can harm the environment), and maximize their crop production efficiently. This experiment also contributes to the broader field of agricultural science by helping establish guidelines for sustainable farming practices that balance productivity and environmental impact.

Potential Additional Factors:

In real-world scenarios, several other factors could influence the outcome, such as:
Soil type: Certain soils might already be nutrient-rich and need less fertilizer.
Water availability: Fertilizer may only be effective if crops receive enough water.
Climate conditions: Temperature, sunlight, and rainfall could also affect yield, making it necessary to control or account for these variables in the experiment.
Thus, the experiment isolates the fertilizer amount as the primary explanatory variable while keeping other factors constant or controlled to see its true effect on crop yield.

In summary:

The explanatory variable explains or causes changes.
The response variable is what changes as a result of variations in the explanatory variable.