Applying bootstrapping regression

Linear regression analysis is used to determine a linear relationship between two variables, x and y. If x is the independent variable, we try to verify if there is a linear relationship with the dependent variable, y: we try to identify the line capable of representing the distribution of points on a two-dimensional plane. If the points corresponding to the observations are close to the line, the model will effectively describe the link between x and y. The lines that can approximate the observations are infinite, but only one of them optimizes the representation of the data. In the case of a linear mathematical relationship, the observations of y can be obtained from a linear function of the observations of x:

In the previous equation, the terms are defined as follows:

• x is the explanatory variable
• is the slope of the line
• is the intercept with the yaxis
• is a random error variable with zero mean
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