Understanding the influence of variables in linear regression

The goal of linear regression is to build a model useful to predict future values based on evidence in the present data. To achieve this objective, we have two types of variables:

• The predictor variables determine the value of a variable for which we want to know the possible future values.
• The result variable is affected by the predictor variables.

The model accuracy depends on the statistical relevance of the relationship between the variables. To test this relevance, we can probe the model's data relationships. Examples of probes include the following:

• Coefficient of determination, or R-squared
• Coefficient of correlation
• t-statistics and p-value
• f-statistics

The statistical tests are necessary to prove that the variables have a relationship that could be useful to build a predictor model. The four probes previously mentioned are used to test the alternate hypothesis...