### What is correlation coefficient?

As covariance only tells about the direction which is not enough to understand the relationship completely, we divide the covariance with standard deviation of x and y respectively and get correlation coefficient which varies between -1 to +1. It is denoted by ‘r’.

Correlation between x and y can be calculated as following:

Where:

### What is Covariance coefficient?

Covariance tells you whether two random variables vary with respect to each other or not. And if they vary together then whether they vary in same direction or in opposite direction with respect to each other. So if both random variables vary in same direction then we say it is positive covariance, however if they vary in opposite direction then it is negative covariance.

Covariance Cov(X,Y) can be calculated as following:

Where:

**Significance of the formula:**

### What are AIC and BIC values, seen at the output summary of Ordinary Least Square (OLs) in statsmodel?

The **Akaike information criterion** (**AIC**) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection.

When a statistical model is used to represent the process that generated the data, the representation will almost never be exact; so some information will be lost by using the model to represent the process. AIC estimates the relative amount of information lost by a given model: the less information a model loses, the higher the quality of that model.

In estimating the amount of information lost by a model, AIC deals with the trade-off between the goodness of fit of the model and the simplicity of the model. In other words, AIC deals with both the risk of overfitting and the risk of underfitting. **we simply choose the model giving smallest AIC over the set of models considered.**

In statistics, the **Bayesian information criterion** (**BIC**) or **Schwarz information criterion** (also **SIC**, **SBC**, **SBIC**) is a criterion for model selection among a finite set of models; the model with the lowest BIC is preferred. It is based, in part, on the likelihood function and it is closely related to the Akaike information criterion (AIC).

When fitting models, it is possible to increase the likelihood by adding parameters, but doing so may result in overfitting. Both BIC and AIC attempt to resolve this problem by introducing a penalty term for the number of parameters in the model; the penalty term is larger in BIC than in AIC.