Parametric coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.53529 0.03186 16.8 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Approximate significance of smooth terms: edf Ref.df F p-value s(X1) 1.818 2.243 0.687 0.5401 s(X2) 1.729 2.080 2.880 0.0675 . s(X3) 1.740 2.110 0.942 0.4003 s(X4) 1.516 1.828 0.973 0.2865 s(X5) 1.727 2.098 0.011 0.9968 s(X6) 2.063 2.478 0.390 0.7171 s(X7) 1.419 1.682 2.056 0.2184 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 R-sq.(adj) = 0.213 Deviance explained = 42.3% GCV = 0.065102 Scale est. = 0.046688 n = 46这个拟合结果，怎么解释

这个拟合结果是一个 GAM（Generalized Additive Model，广义可加模型）的结果。该模型包含了一个截距项和七个平滑项（s(X1)至s(X7)），其中每个平滑项都是一个自变量对因变量的非线性影响，可以理解为对应自变量的局部回归线。每个平滑项的 edf（estimated degrees of freedom，估计自由度）表示了该平滑项的平滑程度，即该平滑项所对应的局部回归线的灵活性。

拟合结果中还包含了每个参数的估计值（Estimate）、标准误差（Std. Error）、t值（t value）和p值（Pr(>|t|)）等信息。其中，t值和p值用于检验每个参数的显著性，p值小于0.05（或0.01、0.001）表示该参数的效应在统计上是显著的。

拟合结果中还包含了模型的拟合优度指标，比如调整后的 R 方值（R-sq.(adj)）和解释差异程度（Deviance explained），以及模型的预测误差估计值，比如广义交叉验证误差（GCV）和标准差估计值（Scale est.）等。

需要注意的是，该拟合结果中有些平滑项的p值较大，表明这些平滑项在统计上并不显著。但是，这并不意味着这些自变量对因变量的影响是线性的，而是可能需要更加灵活的非线性模型来描述。

相关问题

Parametric coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.52314 0.01395 37.5 <2e-16 *** --- Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1 Approximate significance of smooth terms: edf Ref.df F p-value s(X1) 1.976 1.999 11.034 0.000196 *** s(X2) 1.000 1.000 22.669 3.73e-05 *** s(X3) 1.434 1.670 2.187 0.097375 . s(X4) 1.000 1.000 17.832 0.000178 *** s(X5) 1.875 1.974 6.487 0.007730 ** --- Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1 R-sq.(adj) = 0.943 Deviance explained = 95.4% GCV = 0.01 Scale est. = 0.0079798 n = 41解释下

This output is from a generalized linear model (GLM) with smooth terms included. The "Parametric coefficients" section shows the estimated coefficients for the intercept and any predictor variables that were included as parametric terms. The "Approximate significance of smooth terms" section shows the estimated degrees of freedom (edf), reference degrees of freedom (Ref.df), F-statistic, and p-value for each smooth term included in the model. The "Signif. codes" indicate the level of significance for each term. The "R-sq.(adj)" is the adjusted R-squared value, which indicates the proportion of variance explained by the model after adjusting for the number of predictors included. The "Deviance explained" is the percentage of deviance in the response variable that is explained by the model. The "GCV" is the generalized cross-validation score, which is a measure of predictive accuracy. The "Scale est." is the estimated scale parameter for the model, which represents the variability of the response variable that is not explained by the predictors. The "n" is the sample size.

Family: gaussian Link function: identity Formula: Y ~ s(X1) + s(X2) + s(X3) + s(X4) Parametric coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.580617 0.001752 331.4 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Approximate significance of smooth terms: edf Ref.df F p-value s(X1) 7.931 8.730 36.52 < 2e-16 *** s(X2) 1.000 1.000 18.02 0.000959 *** s(X3) 8.952 8.995 81.75 < 2e-16 *** s(X4) 8.985 8.999 34.34 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 R-sq.(adj) = 0.999 Deviance explained = 100% GCV = 0.00039298 Scale est. = 0.00012586 n = 41解释

这是一个广义线性模型，使用高斯分布作为响应变量的分布，使用恒等函数作为联系函数。该模型的公式是Y ~ s(X1) + s(X2) + s(X3) + s(X4)，其中s()代表平滑函数。模型的参数估计值和标准误差都被列出来了，以及t值和p值。平滑项的自由度和参考自由度也被列出来了，以及F值和p值。模型的调整R方为0.999，解释了100%的偏差。GCV和比例估计值也被列出来了，n表示样本量为41。