To increase the R-squared value in polynomial regression, there are several strategies to improve the model’s fit to the data and better capture the underlying relationships between the independent and dependent variables. Some of the approaches to consider are

**Higher Polynomial Degrees:**Increasing the polynomial degree allows the model to capture more complex relationships in the data. However, we have to be cautious not to overfit the data by selecting a degree that is too high.**Feature Engineering:**Adding additional relevant features to the model. New features may help explain more variance in the dependent variable. Domain knowledge can guide in identifying meaningful additional features.**Interaction Terms:**Interaction terms capture the combined effect of two or more independent variables. Including interaction terms can help capture more nuanced relationships in the data.**Outlier Handling:**Identify and address outliers in the dataset. Outliers can disproportionately influence the regression model and reduce R^{2}. We can either remove outliers or use robust regression techniques that are less sensitive to outliers.**Feature Scaling:**Ensure that the features are appropriately scaled. Some algorithms, like polynomial regression, can be sensitive to the scale of the input features. Standardize or normalize the features to have similar scales.**Data Quality:**Ensure that our dataset is of high quality, free from missing values and data errors. Poor data quality can lead to misleading results and lower R-square.**Residual Analysis:**Examine the residuals – the differences between actual and predicted values. We should look for patterns or systematic errors in the residuals. If we find patterns, it may indicate that the model is not capturing some important relationships.**Model Selection:**Consider exploring other regression algorithms or machine learning models that may better suit our data. Different algorithms have different strengths, and one model may perform better than polynomial regression for our specific problem.