Quadratic model is a type of polynomial regression, it is used to define the relationship between a dependent variable and one or more independent variables in the form of quadratic equations. Quadratic model is used for defining the non-linear relationship between the dependent and independent variables. These are useful when the relationship between dependent and independent variables is not linear and it follows U-shaped curve, in this case a quadratic model is a good choice. So, if we suspect that the relationship between the variables is not linear or it follows a U-shaped curve or inverted u shape curve then it Quadratic model is a perfect choice.
Overfitting is a common problem, it occurs when the model is overtrained on the data, i.e. the model learns the train data to well ,where it captures the noise and fluctuations present in the data. The resultant model will wok very well on the training data but it performs very poorly on the testing or unseen data. There are multiple reasons for the cause of overfitting like using a model which is too complex for the data, insufficient data, and noisy data present in the data. To avoid overfitting there are few methods like cross-validation, it is a technique where the dataset is divided into multiple parts and then evaluating for n number of times can help detect overfitting. Choosing the right model (Simpler Model) for the data is important because, if we choose a model which is highly complex to the given dataset then there is chance of overfitting. Collecting more data can help model to generalize better and help reducing the risk of overfitting.