Multiple regression is a statistical method that can be used to examine the relationship between a continuous outcome variable and multiple predictor variables. In multiple regression, the goal is to understand how the predictor variables are related to the outcome variable and to identify any significant relationships between the variables.

To conduct a multiple regression analysis, you will need a dataset that includes both the outcome variable and the predictor variables. The outcome variable should be continuous (e.g., a numerical value), while the predictor variables can be either continuous or categorical. In your case, dengue incidences can be used as the outcome variable, while time, rainfall, and wind flow can be used as predictor variables.

Before conducting a multiple regression analysis, it is important to ensure that your data meets the assumptions of the model. These assumptions include linearity (the relationship between the predictor variables and the outcome variable is linear), homoscedasticity (the variance of the errors is constant across all levels of the predictor variables), and independence of errors (the errors are not correlated with each other). If these assumptions are not met, the results of the analysis may not be reliable.

It is also important to carefully consider the confounding variables that may impact the relationship between the predictor variables and the outcome variable. A confounding variable is a variable that is associated with both the predictor and outcome variables and can confound (or distort) the relationship between them. For example, if there is a strong relationship between rainfall and dengue incidences, but there is also a relationship between temperature and both rainfall and dengue incidences, then temperature could be a confounding variable.

If your data meets the assumptions of the multiple regression model and you have considered the potential confounding variables, you can proceed with the analysis. The results of the multiple regression analysis can help you understand the relative importance of each predictor variable in predicting the outcome variable and can also help you identify any significant relationships between the variables. This information can be useful for understanding the factors that influence dengue incidences and for developing strategies to prevent or mitigate outbreaks.

Overall, multiple regression can be a useful tool for examining the relationship between a continuous outcome variable and multiple predictor variables, but it is important to carefully consider the assumptions of the model and the potential confounding variables before conducting the analysis.

instead you can use ensemble methods such as random forest and decision tree can be used as an alternative to multiple regression for examining the relationship between a continuous outcome variable and multiple predictor variables. These methods are commonly used for both regression and classification tasks in machine learning.

There are several advantages of using random forest and decision tree models over multiple regression for examining the relationship between a continuous outcome variable and multiple predictor variables:

• Ability to handle both continuous and categorical predictor variables: Both random forest and decision tree models can handle both continuous and categorical predictor variables, while multiple regression can only be used with continuous predictor variables. This makes them more flexible and allows you to include a wider range of variables in your analysis.
• Simplicity: Both random forest and decision tree models are relatively simple to implement and interpret, making them a good choice for certain types of problems. In contrast, multiple regression can be more complex to implement and interpret, particularly if there are many predictor variables or if the relationships between the variables are nonlinear.
• Robustness: Both random forest and decision tree models are relatively robust to outliers and other types of noise in the data, which can make them more resistant to overfitting. Multiple regression, on the other hand, can be more sensitive to outliers and can be prone to overfitting if the model is not properly tuned.

Overall, random forest and decision tree models can be useful alternatives to multiple regression for examining the relationship between a continuous outcome variable and multiple predictor variables.

As a hydrological researcher belonging to the field of geosciences, I think it is very reasonable to use time as the independent variable. But I, personally, do not in favor of using rainfall, also known as precipitation, as an independent variable on an annual basis, because there is often seasonal variation in the precipitation process, and in many areas it is common to have large precipitation in the middle months of the year and small precipitation in the beginning and end months of the year, so using year as the independent variable may not be appropriate. However, we can try to use quarter as the time unit.

You can perfectly add time as a variable in your regression. However, if you wish to consider seasonal changes in dengue, it might be more suitable to introduce time as a periodic variable with a 1 yr period. You might also consider using climatic indexes instead or in addition to time.

Yes, you should be able to use time as one of your regression variables. Following the excellent discussion posted by Dr. Herath above, when interpreting the results of multiple regression, you need to consider covariances amongst your regression variables; e.g. precipitation and/or wind may have a statistically significant trend with time over the period of your data. The confidence intervals of the resultant regression coefficients for such co-varying regression variables will be broader; use of variance inflation factors (VIF) could be one approach to estimating the confidence intervals of the regression coefficients of co-varying regression variables.