Residuals of Data Set

single_residual(actual, expected)

Calculates the difference between the actual value and the expected value

Parameters

  • actual (int or float) – Value actually provided by an initial data set

  • expected (int or float) – Value predicted to occur by a generated model at the same input to the one that coincided with the actual value

Raises

TypeError – Arguments must be integers or floats

Returns

residual – Difference between the actual value and the expected value

Return type

float

See also

single_deviation(), correlation_coefficient()

Notes

  • Observed value: \(y\)

  • Predicted value: \(\hat{y}\)

  • Residual: \(e = y - \hat{y}\)

  • Residual

Examples

Import single_residual function from regressions library
>>> from regressions.statistics.residuals import single_residual
Determine the residual between an actual value of 7.8 and an expected value of 9.2
>>> residual_small = single_residual(7.8, 9.2)
>>> print(residual_small)
-1.3999999999999995
Determine the residual between an actual value of 6.1 and an expected value of 19.8
>>> residual_large = single_residual(6.1, 19.8)
>>> print(residual_large)
-13.700000000000001
multiple_residuals(actual_array, expected_array)

Generates a list of the differences between the actual values from one list and the expected values from another list

Parameters

  • actual_array (list of int or float) – List containing the actual values observed from a data set

  • expected_array (list of int or float) – List containing the expected values predicted for a data set

Raises

  • TypeError – Arguments must be 1-dimensional lists

  • TypeError – Elements of arguments must be integers or floats

  • ValueError – Both arguments must contain the same number of elements

Returns

residuals – Differences between the actual values and the expected values

Return type

list of float

See also

multiple_deviations(), correlation_coefficient()

Notes

  • Observed values: \(y_i = \{ y_1, y_2, \cdots, y_n \}\)

  • Predicted values: \(\hat{y}_i = \{ \hat{y}_1, \hat{y}_2, \cdots, \hat{y}_n \}\)

  • Residuals: \(e_i = \{ y_1 - \hat{y}_1, y_2 - \hat{y}_2, \cdots, y_n - \hat{y}_n \}\)

  • Residual

Examples

Import multiple_residuals function from regressions library
>>> from regressions.statistics.residuals import multiple_residuals
Determine the residuals between the actual values [5.6, 8.1, 6.3] and the expected values [6.03, 8.92, 6.12]
>>> residuals_short = multiple_residuals([5.6, 8.1, 6.3], [6.03, 8.92, 6.12])
>>> print(residuals_short)
[-0.4300000000000006, -0.8200000000000003, 0.17999999999999972]
Determine the residuals between the actual values [11.7, 5.6, 8.1, 13.4, 6.3] and the expected values [15.17, 6.03, 8.92, 9.42, 6.12]
>>> residuals_long = multiple_residuals([11.7, 5.6, 8.1, 13.4, 6.3], [15.17, 6.03, 8.92, 9.42, 6.12])
>>> print(residuals_long)
[-3.4700000000000006, -0.4300000000000006, -0.8200000000000003, 3.9800000000000004, 0.17999999999999972]