It is possible that there could be an interaction between the nitrogen and phosphorus variables in their effect on crop yield. This means that the effect of one variable on crop yield may depend on the level of the other variable.
For example, if there is already an adequate amount of phosphorus in the soil, adding more nitrogen may not have a significant impact on crop yield. However, if there is a deficiency of phosphorus, adding nitrogen may have a greater impact on increasing crop yield. Therefore, it would be important to examine the data and analyze the relationship between crop yield and the two fertilizer variables to determine if there is indeed an interaction effect present.
When examining the response variable Y (crop yield in bushels per acre) and its relationship with the predictor variables nitrogen and phosphorus applied per acre, it's important to consider whether there might be an interaction between these two fertilizer variables. An interaction would imply that the effect of one predictor variable (e.g., nitrogen) on crop yield depends on the level of the other predictor variable (e.g., phosphorus).
Explanation:
1. Identify the variables:
- Response variable (Y): Crop yield in bushels per acre
- Predictor variables: Nitrogen and phosphorus applied per acre
2. Analyze the relationship between crop yield and the fertilizer variables:
- It's reasonable to expect that applying nitrogen or phosphorus individually could have a positive effect on crop yield, as these nutrients are essential for plant growth.
- However, plants often require a specific balance of nutrients for optimal growth. This means that the effect of nitrogen on crop yield might depend on the level of phosphorus, and vice versa.
3. Determine if an interaction is present:
- If applying both nitrogen and phosphorus simultaneously results in a higher (or lower) crop yield than expected based on their individual effects, this would indicate an interaction between the two fertilizer variables.
In conclusion, it is possible that an interaction between nitrogen and phosphorus applied per acre exists when predicting crop yield. To confirm this, you would need to conduct a statistical analysis of relevant data.