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Answers for “如何决定从曲线拟合模型中删除哪些变量?”

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You decide which variables to remove by examining their p-values. If a predictor variable has a p-value greater than a chosen significance level (commonly 0.05), it is considered not statistically significant.

Conditions: Significance level is typically set to 0.05.; The model includes multiple predictor variables with associated p-values.

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To compare different curve fitting approaches, you should use statistical metrics such as R-squared, Adjusted R-squared, Root Mean Square Error (RMSE), and Sum of Squared Errors (SSE). R-squared measures the proportion of variance explained by the model, while RMSE and SSE measure the average magnitude of the errors, with lower values indicating a better fit.

Conditions: Two or more curve fitting models are being evaluated.; The models are fitted to the same dataset.

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You can force your curve fit to respect physical limits by formulating it as a constrained optimization problem using the Optimization Toolbox. Define the model coefficients as optimization variables and assign specific lower and upper bounds to each coefficient.

Conditions: Requires an optimization solver like lsqnonlin.; Objective function must be defined based on the model equation (e.g., minimizing sum of squared errors).; Physical or mathematical constraints on coefficients are known.

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In the fitted wind-turbine model shown in the clip, wind speed has a much larger effect on predicted power output than wind direction, air density, turbulence, or wind shear. This is evidenced by the steep S-shaped curve for wind speed in the Plot Slice window, whereas the curves for the other factors are nearly horizontal, indicating very small impacts.

Conditions: The analysis is based on the specific dataset and fitted model shown in the video segment.; A nonlinear model has been fitted using wind speed plus four other factors.

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The Plot Slice window displays separate panels for each predictor variable in a fitted multi-factor model. To compare impacts, observe the steepness of the curve in each panel.

Conditions: A fitted model with multiple predictors is available.; The software can generate partial-effect style plots for each predictor.

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The nonlinear model combines a sigmoidal dependence on wind speed with assumed linear contributions from additional wind-related factors. Mathematically, it is expressed as P=b11+exp⁡(−b2(x1−b3))+b4x2+b5x3+b6x4+b7x5P = \frac{b_1}{1+\exp(-b_2(x_1-b_3))} + b_4 x_2 + b_5 x_3 + b_6 x_4 + b_7 x_5, where x1x_1 represents wind speed, and x2x_2 through x5x_5 represent other factors like wind direction, air density, turbulence, and wind shear.

Conditions: Multiple predictor factors are to be modeled together.; Wind speed is known to have a sigmoidal relation to power output.; Other factors are assumed linear for simplicity.