量化模型拟合
R 中的回归入门
Richie Cotton
Data Evangelist at DataCamp
鲷与鲈的模型
鲷（Bream）
鲈（Perch）
判定系数
也称为"r 方"或"R 方"。
响应变量方差中可由解释变量预测的比例
1表示完美拟合0表示最差拟合
summary()
查看名为"Multiple R-Squared"的值
mdl_bream <- lm(mass_g ~ length_cm, data = bream)
summary(mdl_bream)
# 省略部分输出
Residual standard error: 74.15 on 33 degrees of freedom
Multiple R-squared: 0.8781, Adjusted R-squared: 0.8744
F-statistic: 237.6 on 1 and 33 DF, p-value: < 2.2e-16
glance()
library(broom)
library(dplyr)
mdl_bream %>%
glance()
# A tibble: 1 × 12
r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 0.878 0.874 74.2 238. 1.22e-16 1 -199. 405. 409.
# ... with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
mdl_bream %>%
glance() %>%
pull(r.squared)
0.8780627
就是相关系数的平方
bream %>%
summarize(
coeff_determination = cor(length_cm, mass_g) ^ 2
)
coeff_determination
1 0.8780627
残差标准误（RSE）
预测与观测响应之间的"典型"差异
其单位与响应变量相同。
再次使用 summary()
查看名为"Residual standard error"的值
summary(mdl_bream)
# 省略部分输出
Residual standard error: 74.15 on 33 degrees of freedom
Multiple R-squared: 0.8781, Adjusted R-squared: 0.8744
F-statistic: 237.6 on 1 and 33 DF, p-value: < 2.2e-16
再次使用 glance()
library(broom)
library(dplyr)
mdl_bream %>%
glance()
# A tibble: 1 x 11
r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual
<dbl> <dbl> <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl> <int>
1 0.878 0.874 74.2 238. 1.22e-16 2 -199. 405. 409. 181452. 33
mdl_bream %>%
glance() %>%
pull(sigma)
74.15224
计算 RSE：残差平方
bream %>%
mutate(
residuals_sq = residuals(mdl_bream) ^ 2
)
species mass_g length_cm residuals_sq
1 Bream 242 23.2 138.9571
2 Bream 290 24.0 260.7586
3 Bream 340 23.9 5126.9926
4 Bream 363 26.3 1318.9197
5 Bream 430 26.5 390.9743
6 Bream 450 26.8 547.9380
...
计算 RSE：残差平方和
bream %>%
mutate(
residuals_sq = residuals(mdl_bream) ^ 2
) %>%
summarize(
resid_sum_of_sq = sum(residuals_sq)
)
resid_sum_of_sq
1 181452.3
计算 RSE：自由度
自由度等于观测数减去模型系数数。
bream %>%
mutate(
residuals_sq = residuals(mdl_bream) ^ 2
) %>%
summarize(
resid_sum_of_sq = sum(residuals_sq),
deg_freedom = n() - 2
)
resid_sum_of_sq deg_freedom
1 181452.3 33
计算 RSE：比值开方
bream %>%
mutate(
residuals_sq = residuals(mdl_bream) ^ 2
) %>%
summarize(
resid_sum_of_sq = sum(residuals_sq),
deg_freedom = n() - 2,
rse = sqrt(resid_sum_of_sq / deg_freedom)
)
resid_sum_of_sq deg_freedom rse
1 181452.3 33 74.15224
解释 RSE
mdl_bream 的 RSE 为 74。
预测的鲷鱼质量与观测质量的差异通常约为 74g。
均方根误差（RMSE）
残差标准误
bream %>%
mutate(
residuals_sq = residuals(mdl_bream) ^ 2
) %>%
summarize(
resid_sum_of_sq = sum(residuals_sq),
deg_freedom = n() - 2,
rse = sqrt(resid_sum_of_sq / deg_freedom)
)
均方根误差
bream %>%
mutate(
residuals_sq = residuals(mdl_bream) ^ 2
) %>%
summarize(
resid_sum_of_sq = sum(residuals_sq),
n_obs = n(),
rmse = sqrt(resid_sum_of_sq / n_obs)
)
Passons à la pratique !
R 中的回归入门
