原文：https://mp.weixin.qq.com/s/SGIvgqX7mLv563fqYmze9g
简介
- 建立平均每周锻炼时间（minute）与平均肺活量（VC ）回归方程
- 输入：
minute <- c(110,118,120,123,131,137,144,149,152,160)
VC <- c(5283,5299,5358,5292,5602,6014,5830,6102,6075,6411)
lrdata <- data.frame(minute,VC)
modelle <- lm(VC~minute,data=lrdata)
summary(modelle)
- 结果：
Call:
lm(formula = VC ~ minute, data = lrdata)
Residuals:
Min 1Q Median 3Q Max
-162.71 -64.39 -30.81 62.18 225.39
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2521.184 342.088 7.370 7.84e-05 ***
minute 23.850 2.528 9.435 1.31e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 126.2 on 8 degrees of freedom
Multiple R-squared: 0.9175, Adjusted R-squared: 0.9072
F-statistic: 89.01 on 1 and 8 DF, p-value: 1.309e-05
- 输入：
cbind( coef=coef(modelle), confint(modelle))
- 结果：
coef 2.5 % 97.5 %
(Intercept) 2521.18375 1732.32765 3310.03985
minute 23.84982 18.02041 29.67924
- 输入：
predict(modelle,newdata=data.frame(minute=c(140,145,150)),interval = "confidence")
#求给定minute下VC均值的预测值和置信区间
- 结果：
fit lwr upr
1 5860.159 5762.545 5957.773
2 5979.408 5868.588 6090.228
3 6098.657 5969.302 6228.013
- 输入：
library(ggplot2)
pre <- predict(modelle,newdata=data.frame(minute),interval = "prediction") int <- predict(modelle,newdata=data.frame(minute),interval = "confidence")
# 求个值的预测区间:interval = {"none","prediction","confidence"}分别表示预测值、预测值+预测区间、预测值加期望值 # 举例：95% 置信区间：(562.931, 575.483)，95% 预测区间：(556.186, 582.227) # 置信区间解释为：有95%的把握断言，断裂强度平均值将落入（562.931,575.438）之内； # 预测区间解释为：95%的把握断言，任何一块钢板的断裂强度将落入（556.186,582.227）之内，一般还是使用预测区间；newlr <- cbind(lrdata,pre)ggplot(newlr,aes(x=minute,y=VC))+geom_point(size=3,colour="blue")+ # 原始数据点图
geom_segment(aes(x=minute, xend=minute, y=VC, yend=fit),size=1,linetype=2,colour="red")+ # 预测值～实际值虚线
geom_smooth(method=lm,se=T)+ # 添加拟合图形，其中包括模型曲线、置信区间
geom_line(aes(y=lwr), color = "red", linetype = "dashed",size=1)+ # 模型预测区间的下沿
geom_line(aes(y=upr), color = "red", linetype = "dashed",size=1) # 模型预测区间的上沿
- 结果：
以下内容，暂时没有学习
标化回归系数——方法1：
- 输入：
install.packages("sjstats")
library(sjstats)
std_beta(modelle,type="std",ci.lvl=0.95)
- 结果：
term std.estimate std.error conf.low conf.high
minute 0.958 0.102 0.759 1.16
标化回归系数——方法2：
- 输入：
install.packages("lm.beta")
library(lm.beta)
stdco <- lm.beta(modelle)
summary(stdco)
- 结果：
Call:
lm(formula = VC ~ minute, data = lrdata)
Residuals:
Min 1Q Median 3Q Max
-162.71 -64.39 -30.81 62.18 225.39
Coefficients:
Estimate Standardized Std. Error t value Pr(>|t|)
(Intercept) 2521.1837 0.0000 342.0879 7.370 7.84e-05 ***
minute 23.8498 0.9579 2.5279 9.435 1.31e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 126.2 on 8 degrees of freedom
Multiple R-squared: 0.9175, Adjusted R-squared: 0.9072
F-statistic: 89.01 on 1 and 8 DF, p-value: 1.309e-05