Generate All Models

run_all(data, precision=4)

Generates all eight key regression models (linear, quadratic, cubic, hyperbolic, exponential, logarithmic, logistic, and sinusoidal) for a given data set, in addition to determining the best fit based on correlation and providing various statistical measures

Parameters

  • data (list of lists of int or float) – List of lists of numbers representing a collection of coordinate pairs; it must include at least 10 pairs

  • precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the results

Raises

  • TypeError – First argument must be a 2-dimensional list

  • TypeError – Elements nested within first argument must be integers or floats

  • ValueError – First argument must contain at least 10 elements

  • ValueError – Last argument must be a positive integer

Returns

  • results[‘models’][‘linear’] (dict) – See Linear Model

  • results[‘models’][‘quadratic’] (dict) – See Quadratic Model

  • results[‘models’][‘cubic’] (dict) – See Cubic Model

  • results[‘models’][‘hyperbolic’] (dict) – See Hyperbolic Model

  • results[‘models’][‘exponential’] (dict) – See Exponential Model

  • results[‘models’][‘logarithmic’] (dict) – See Logarithmic Model

  • results[‘models’][‘logistic’] (dict) – See Logistic Model

  • results[‘models’][‘sinusoidal’] (dict) – See Sinusoidal Model

  • results[‘statistics’][‘minimum’] (int or float) – Smallest value of the independent variable from the provided data set

  • results[‘statistics’][‘maximum’] (int or float) – Largest value of the independent variable from the provided data set

  • results[‘statistics’][‘q1’] (int or float) – First quartile of the independent variable from the provided data set, below which 25% of the data points lie

  • results[‘statistics’][‘q3’] (int or float) – Third quartile of the independent variable from the provided data set, above which 25% of the data points lie

  • results[‘statistics’][‘mean’] (int or float) – Arithmetic mean of the independent variable from the provided data set

  • results[‘statistics’][‘median’] (int or float) – Median of the independent variable from the provided data set, which splits the data in half

  • results[‘optimal’][‘option’] (str) – Name of the model with the highest correlation for this particular data set (e.g., ‘cubic’ if the cubic model has a higher correlation than all other seven models)

  • results[‘optimal’][‘correlation’] (float) – Value of the correlation for the model with the best fit (i.e., the model listed in [‘optimal’][‘option’])

See also

linear_model(), quadratic_model(), cubic_model(), hyperbolic_model(), exponential_model(), logarithmic_model(), logistic_model(), sinusoidal_model(), five_number_summary(), correlation_coefficient()

Notes

  • Provided ordered pairs for the data set: \(p_i = \{ (p_{1,x}, p_{1,y}), (p_{2,x}, p_{2,y}), \cdots, (p_{n,x}, p_{n,y}) \}\)

  • Provided values for the independent variable: \(X_i = \{ p_{1,x}, p_{2,x}, \cdots, p_{n,x} \}\)

  • Provided values for the dependent variable: \(Y_i = \{ p_{1,y}, p_{2,y}, \cdots, p_{n,y} \}\)

  • Resultant values for the coefficients of the linear model: \(C_{lin} = \{ a_{lin}, b_{lin} \}\)

  • Standard form for the equation of the linear model: \(lin(x) = a_{lin}\cdot{x} + b_{lin}\)

  • Resultant values for the coefficients of the quadratic model: \(C_{quad} = \{ a_{quad}, b_{quad}, c_{quad} \}\)

  • Standard form for the equation of the quadratic model: \(quad(x) = a_{quad}\cdot{x^2} + b_{quad}\cdot{x} + c_{quad}\)

  • Resultant values for the coefficients of the cubic model: \(C_{cub} = \{ a_{cub}, b_{cub}, c_{cub}, d_{cub} \}\)

  • Standard form for the equation of the cubic model: \(cub(x) = a_{cub}\cdot{x^3} + b_{cub}\cdot{x^2} + c_{cub}\cdot{x} + d_{cub}\)

  • Resultant values for the coefficients of the hyperbolic model: \(C_{hyp} = \{ a_{hyp}, b_{hyp} \}\)

  • Standard form for the equation of the hyperbolic model: \(hyp(x) = a_{hyp}\cdot{\frac{1}{x}} + b_{hyp}\)

  • Resultant values for the coefficients of the exponential model: \(C_{exp} = \{ a_{exp}, b_{exp} \}\)

  • Standard form for the equation of the exponential model: \(exp(x) = a_{exp}\cdot{b_{exp}^x}\)

  • Resultant values for the coefficients of the logarithmic model: \(C_{log} = \{ a_{log}, b_{log} \}\)

  • Standard form for the equation of the logarithmic model: \(log(x) = a_{log}\cdot{\ln{x}} + b_{log}\)

  • Resultant values for the coefficients of the logistic model: \(C_{lst} = \{ a_{lst}, b_{lst}, c_{lst} \}\)

  • Standard form for the equation of the logistic model: \(lst(x) = \frac{a_{lst}}{1 + \text{e}^{-b_{lst}\cdot(x - c_{lst})}}\)

  • Resultant values for the coefficients of the sinusoidal model: \(C_{sin} = \{ a_{sin}, b_{sin}, c_{sin}, d_{sin} \}\)

  • Standard form for the equation of the sinusoidal model: \(sin(x) = a_{sin}\cdot{\sin(b_{sin}\cdot(x - c_{sin}))} + d_{sin}\)

  • Regression Analysis

Examples

Import run_all function from regressions library
>>> from regressions.execute import run_all
Generate all eight regression models for the data set [[1, 32], [2, 25], [3, 14], [4, 23], [5, 39], [6, 45], [7, 42], [8, 49], [9, 36], [10, 33]], then print each model’s coefficients, the mean of the data set, and the name of the model with the best fit
>>> results = run_all([[1, 32], [2, 25], [3, 14], [4, 23], [5, 39], [6, 45], [7, 42], [8, 49], [9, 36], [10, 33]])
>>> print(results['models']['linear']['constants'])
[1.9636, 23.0]
>>> print(results['models']['quadratic']['constants'])
[-0.3106, 5.3803, 16.1667]
>>> print(results['models']['cubic']['constants'])
[-0.3881, 6.0932, -24.155, 49.4667]
>>> print(results['models']['hyperbolic']['constants'])
[-13.5246, 37.7613]
>>> print(results['models']['exponential']['constants'])
[22.1049, 1.0692]
>>> print(results['models']['logarithmic']['constants'])
[7.4791, 22.5032]
>>> print(results['models']['logistic']['constants'])
[43.9838, 0.3076, 0.9747]
>>> print(results['models']['sinusoidal']['constants'])
[14.0875, 0.7119, -3.7531, 34.2915]
>>> print(results['statistics']['mean'])
5.5
>>> print(results['optimal']['option'])
'sinusoidal'
Generate all eight regression models for the data set [[169, 423], [122, 391], [178, 555], [131, 284], [120, 520], [179, 558], [164, 265], [167, 338], [198, 445], [139, 402], [183, 725], [133, 470], [156, 573], [159, 325], [121, 653], [118, 358], [122, 633], [167, 487], [161, 453], [194, 488], [170, 517], [124, 377], [191, 310], [194, 398], [173, 744], [166, 389], [113, 583], [109, 380], [126, 668], [144, 491], [107, 533], [188, 355], [147, 553], [169, 497], [121, 606], [132, 373], [111, 554], [173, 669], [177, 483], [122, 340], [171, 286], [108, 681], [139, 502], [115, 339], [174, 396], [134, 625], [147, 435], [146, 555], [147, 656], [126, 354], [155, 679], [181, 629], [149, 417], [119, 374], [102, 422], [112, 292], [108, 464], [109, 559], [112, 635], [159, 518], [180, 304], [185, 567], [165, 299], [160, 337], [133, 730], [193, 374], [164, 537], [172, 592], [173, 660], [186, 290], [170, 670], [192, 687], [154, 596], [154, 464], [125, 383], [193, 559], [155, 586], [149, 406], [131, 590], [127, 339], [163, 378], [145, 254], [156, 395], [166, 355], [189, 661], [133, 685], [168, 685], [190, 736], [145, 564], [125, 470], [129, 541], [133, 439], [162, 486], [125, 387], [183, 596], [135, 733], [106, 329], [100, 279], [102, 439], [162, 454]], then print each model’s coefficients, the mean of the data set, and the name of the model with the best fit
>>> results_large = run_all([[169, 423], [122, 391], [178, 555], [131, 284], [120, 520], [179, 558], [164, 265], [167, 338], [198, 445], [139, 402], [183, 725], [133, 470], [156, 573], [159, 325], [121, 653], [118, 358], [122, 633], [167, 487], [161, 453], [194, 488], [170, 517], [124, 377], [191, 310], [194, 398], [173, 744], [166, 389], [113, 583], [109, 380], [126, 668], [144, 491], [107, 533], [188, 355], [147, 553], [169, 497], [121, 606], [132, 373], [111, 554], [173, 669], [177, 483], [122, 340], [171, 286], [108, 681], [139, 502], [115, 339], [174, 396], [134, 625], [147, 435], [146, 555], [147, 656], [126, 354], [155, 679], [181, 629], [149, 417], [119, 374], [102, 422], [112, 292], [108, 464], [109, 559], [112, 635], [159, 518], [180, 304], [185, 567], [165, 299], [160, 337], [133, 730], [193, 374], [164, 537], [172, 592], [173, 660], [186, 290], [170, 670], [192, 687], [154, 596], [154, 464], [125, 383], [193, 559], [155, 586], [149, 406], [131, 590], [127, 339], [163, 378], [145, 254], [156, 395], [166, 355], [189, 661], [133, 685], [168, 685], [190, 736], [145, 564], [125, 470], [129, 541], [133, 439], [162, 486], [125, 387], [183, 596], [135, 733], [106, 329], [100, 279], [102, 439], [162, 454]])
>>> print(results_large['models']['linear']['constants'])
[0.4934, 414.5401]
>>> print(results_large['models']['quadratic']['constants'])
[-0.007, 2.5668, 265.4919]
>>> print(results_large['models']['cubic']['constants'])
[0.0005, -0.2204, 33.8099, -1226.1398]
>>> print(results_large['models']['hyperbolic']['constants'])
[-10786.2465, 563.019]
>>> print(results_large['models']['exponential']['constants'])
[407.8094, 1.0009]
>>> print(results_large['models']['logarithmic']['constants'])
[74.0076, 118.997]
>>> print(results_large['models']['logistic']['constants'])
[878.3475, 0.0023, 51.0002]
>>> print(results_large['models']['sinusoidal']['constants'])
[32.3199, 1.0085, 1.8848, 488.9635]
>>> print(results_large['statistics']['mean'])
149.29
>>> print(results_large['optimal']['option'])
'sinusoidal'