Final answer:
A simple linear regression model to understand the relationship between nitrogen fertilizer and corn yield would use nitrogen as the independent variable and yield as the dependent variable. The equation might be Õ = 20 + 5x, representing a base yield of 20 bushels per acre, with each unit of nitrogen potentially increasing yield by 5 bushels.
Step-by-step explanation:
To understand if nitrogen fertilizer increases corn yields more when rainfall is greater using simple linear regression, we can establish a model where:
- Nitrogen amount (fertilizer) is the independent variable (x).
- Corn yield (in bushels per acre) is the dependent variable (y).
The simple linear regression equation would be:
Õ = a + bx
Where:
- Õ is the predicted corn yield.
- a is the y-intercept, representing the expected yield without additional nitrogen.
- b is the slope, representing the increase in yield per unit of nitrogen added.
- x is the amount of nitrogen applied.
For a hypothetical scenario, assuming the presence of adequate rainfall, the equation could be:
Õ = 20 + 5x
This equation suggests that for every unit of nitrogen applied, there is an expected increase of 5 bushels per acre of corn, starting at a base yield of 20 bushels per acre without added nitrogen.
To visually interpret this, draw a scatter plot with points representing different amounts of nitrogen and corresponding yields. The regression line would be a straight line that best fits the data points. The slope of this line would indicate the relationship between fertilizer application and increased corn yield.