{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For compatibility with older versions of SciPy, the return value acts like a " }, { "__type": "InlineCode", "__tag": 4051, "value": "namedtuple" }, { "__type": "Text", "__tag": 4046, "value": " of length 5, with fields " }, { "__type": "InlineCode", "__tag": 4051, "value": "slope" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "intercept" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "rvalue" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "pvalue" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "stderr" }, { "__type": "Text", "__tag": 4046, "value": ", so one can continue to write " } ] }, { "__type": "Code", "__tag": 4050, "value": "slope, intercept, r, p, se = linregress(x, y)", "execution_status": null, "out": "" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "With that style, however, the standard error of the intercept is not available. 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"success", "out": "" }, { "__type": "Text", "__tag": 4046, "value": "\nGenerate some data:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "x = rng.random(10)\ny = 1.6*x + rng.random(10)\n", "execution_status": "success", "out": "" }, { "__type": "Text", "__tag": 4046, "value": "\nPerform the linear regression:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res = stats.linregress(x, y)\n", "execution_status": "success", "out": "" }, { "__type": "Text", "__tag": 4046, "value": "\nCoefficient of determination (R-squared):\n\n" }, { "__type": "Code", "__tag": 4050, "value": "print(f\"R-squared: {res.rvalue**2:.6f}\")\n", "execution_status": "failure", "out": "R-squared: 0.752698\n" }, { "__type": "Text", "__tag": 4046, "value": "\nPlot the data along with the fitted line:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.plot(x, y, 'o', label='original data')\nplt.plot(x, res.intercept + res.slope*x, 'r', label='fitted line')\nplt.legend()\n", "execution_status": "failure", "out": "\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.show()\n", "execution_status": "success", "out": "" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "2.0.0.dev0+git20260907.41eeb59", "kind": "assets", "path": "fig-b2886baee3b396d4.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nCalculate 95% confidence interval on slope and intercept:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.stats import t\ntinv = lambda p, df: abs(t.ppf(p/2, df))\n", "execution_status": "success", "out": "" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "ts = tinv(0.05, len(x)-2)\n", "execution_status": "success", "out": "" }, { "__type": "Code", "__tag": 4050, "value": "print(f\"slope (95%): {res.slope:.6f} +/- {ts*res.stderr:.6f}\")\nprint(f\"intercept (95%): {res.intercept:.6f}\"\n f\" +/- {ts*res.intercept_stderr:.6f}\")\n", 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