| 1 | /**
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| 2 | * The [R Squared](http://en.wikipedia.org/wiki/Coefficient_of_determination)
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| 3 | * value of data compared with a function `f`
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| 4 | * is the sum of the squared differences between the prediction
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| 5 | * and the actual value.
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| 6 | *
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| 7 | * @param {Array<Array<number>>} x input data: this should be doubly-nested
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| 8 | * @param {Function} func function called on `[i][0]` values within the dataset
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| 9 | * @returns {number} r-squared value
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| 10 | * @example
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| 11 | * var samples = [[0, 0], [1, 1]];
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| 12 | * var regressionLine = linearRegressionLine(linearRegression(samples));
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| 13 | * rSquared(samples, regressionLine); // = 1 this line is a perfect fit
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| 14 | */
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| 15 | function rSquared(x, func) {
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| 16 | if (x.length < 2) {
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| 17 | return 1;
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| 18 | }
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| 19 |
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| 20 | // Compute the average y value for the actual
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| 21 | // data set in order to compute the
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| 22 | // _total sum of squares_
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| 23 | let sum = 0;
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| 24 | for (let i = 0; i < x.length; i++) {
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| 25 | sum += x[i][1];
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| 26 | }
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| 27 | const average = sum / x.length;
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| 28 |
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| 29 | // Compute the total sum of squares - the
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| 30 | // squared difference between each point
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| 31 | // and the average of all points.
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| 32 | let sumOfSquares = 0;
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| 33 | for (let j = 0; j < x.length; j++) {
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| 34 | sumOfSquares += Math.pow(average - x[j][1], 2);
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| 35 | }
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| 36 |
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| 37 | // Finally estimate the error: the squared
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| 38 | // difference between the estimate and the actual data
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| 39 | // value at each point.
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| 40 | let err = 0;
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| 41 | for (let k = 0; k < x.length; k++) {
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| 42 | err += Math.pow(x[k][1] - func(x[k][0]), 2);
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| 43 | }
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| 44 |
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| 45 | // As the error grows larger, its ratio to the
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| 46 | // sum of squares increases and the r squared
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| 47 | // value grows lower.
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| 48 | return 1 - err / sumOfSquares;
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| 49 | }
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| 50 |
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| 51 | export default rSquared;
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