Correlation | Linear Regression | Variance and Standard Deviation

Calculator Linear Regression

Calculates the simple linear regression, i.e. a straight line that predicts the points of a data set with two sizes as well as possible. If you have two connected quantifiable characteristics, such as height and weight of people, and enter many different values of these sizes in a diagram, then the result is a point cloud in which the points are not randomly distributed, but have a direction. This direction can be represented by a straight line.

Please enter the values ​​of the two characteristics separately. For each characteristic, the values ​​must be separated from one another with a blank or a line break. The number of values ​​per characteristic must be the same. The n-th value of the first feature belongs to the n-th value of the second feature. Example calculates with the size (in 1000 km²) and population (in millions) of some European countries.

Characteristic x

Characteristic y

Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Result

Number of value pairs:
Mean value x:
Mean value y:
Intercept β0:
Slope β1:
Regression line f:

The formulas are:

n: number of value pairs, Σ: sum i=1 to n
x: mean values of all x_i, y: mean values of all y_i

β₁ = Σ[(x_i−x)*(y_i−y)] / Σ(x_i−x)²

β₀ = y − β₁*x

f = β₀ + β₁x_i

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