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Linear Regression - calculator with explanation

With this statistical calculator, you will learn how to calculate a linear regression step by step.

Linear Regression - calculator with explanation

Linear Regression information

Linear regression - in statistics, a method of estimating the value of the expected variable y with the known values of another variable or variables. The searched variable y is traditionally called the dependent or dependent variable. The other x variables are called explanatory or independent variables. Both the explanatory and explanatory variables can be scalar quantities or vectors.
Regression in general is a problem of conditional expected value estimation. Linear regression is called linear because the assumed model of the relationship between dependent and independent variables is a linear function.

If there is a linear relationship between two physical quantities (and it can almost always be so, only properly select the axes of the plot) linear regression is a simple (though laborious) method of determining the parameters preferably fitted straight. The obtained fit parameters can then be used to determine the physical quantity sought.

The parameters of the line defined by the equation y = ax + b can be determined using formulas:

a = \frac{n \sum x_{n} y_{n} - \sum x_{n} \sum y_{n}}{n \sum x_{n}^{2} - (\sum x_{n})^{2}}

b = \frac{n \sum y_{n} - a \sum x_{n}}{n}

n - number of observations
x_n, y_n - experimental values
a - slope of the regression line
b - the intersection of the regression line with the Y axis

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