Final answer:
Generating polynomial features can help to uncover new relationships between features and the target, and improve model performance by capturing non-linearities. However, care must be taken to avoid overfitting. These features are especially useful when the relationships in the data are not just linear.
Step-by-step explanation:
Reasons why one would want to generate polynomial features when building a model include:
Uncover new relationships between the features and the target: Polynomial features can provide a more nuanced view of data by allowing for more complex relationships than linear ones. By creating polynomial and interaction terms, we may discover non-linear relationships that help explain variability in the data.
Improve the model's performance: When non-linearity exists between features and the target, polynomial features can capture this, potentially leading to better model performance. However, this must be balanced against the risk of overfitting.
To investigate relationships between two variables, such as the scores of a student's second math exam and their final exam, one should:
Define the independent and dependent variable, typically the independent variable is the one believed to influence the other.
Draw a scatter plot to visually assess the relationship.
Use regression analysis to find the line of best fit (least squares line).
Calculate and interpret the correlation coefficient to understand the strength and direction of the linear relationship.
Consider if a linear model is appropriate or if a more complex model is warranted.
The relationship between variables might not always be linear. That's when polynomial features can enhance model capacity to fit data more accurately. Yet, it's crucial to evaluate the model to prevent overfitting and ensure it generalizes well to new data.