The linear regression model is an easy predictive technique. This model can be as simple as having one input variable and one output variable or as complex as having dozens of input variables. All linear regression models fit this pattern: Independent variables are used first to model and then to predict the result—the dependent variable. In matrix notation, a linear regression model is given by the formula Y = Xβ + Ϲ, where:
- X is the independent (predictor) variable or vector.
- β is the vector of parameters.
- ε is the error vector.
- Y is the dependent (response) vector.
That is:
The input table contains all the predictor columns and, in its last column, the response vector. The output table contains the beta coefficients (in the coefficient_index column). The 0th coefficient corresponds to the slope intercept and the ith coefficient corresponds to the ith predictor variable. The LinReg function is limited to outputting the coefficients; it does not give the significance of predictor variables by a p-value or the goodness of fit by an R2 value.