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❖Simple Regression

Regression analysis is a widely used analytical model, which is mainly used to express the functional relationship between dependent variable (Y) and independent variable (X). When the dependent variable and the independent variable are linear, that is, the first linear relationship of one variable, the graph of dependent variable (Y) and independent variable (X) is expressed as a straight line. The function of linear regression is y = a x + b, where y is dependent variable, x is independent variable, A and B are constant. If the exponent (power) of the independent variable is greater than 1, the relationship between the dependent variable (Y) and the independent variable (X) is non-linear, and the graph is expressed as a curve.

[Independent Variable] x, select the fields to be used as independent variables from the drop-down list.

[Dependent Variable] y, select the fields to be used as dependent variables from the drop-down list.

[Polynomial power] denotes the N power function relationship between independent variables and dependent variables. By default, it is 1. If it is 2, it denotes the quadratic function relationship of one variable.

[Output Value] [Fit Value]: When checked, a Fit Value field is obtained. After the regression model is obtained from the training data, the given sample values (x1, x2,..., xn) are predicted. The predicted results are fitted values, which are estimated values of (y1, y2,..., yn).

[Output Value] [Residual]: When checked, a residual field is obtained. The result is that the actual value of Y is subtracted from the fitting value.

[Output Value] [Confidence Interval]: When checked, the range of confidence interval is calculated according to Level. The default level is 95%.

 

•For Example

Monadic Linear Regression is performed on a series of height and weight values. Collect a series of height and weight values. Height is an independent variable, and weight is dependent variable. Use Simple regression analysis algorithm to get the mathematical equation of the created model. Calculate the fitting value of weight according to mathematical equation.

 

The output result is as shown in the figure: