请准确无误地写出R语言代码完成以下任务:①生成50×30的随机数据集和30个变量;②要生成三组线性模型的①,且这三组原始模型的系数不同;③(线性回归)分别计算这三组的CV值;④(岭回归)分别对这三组,画出CV error图和Prediction error图;⑤基于一倍标准差准则给出参数值上限
时间: 2024-02-21 20:00:37 浏览: 65
以下是R语言代码完成以上任务:
```
set.seed(123)
data <- matrix(rnorm(1500), nrow=50, ncol=30)
colnames(data) <- paste0("Var", 1:30)
set.seed(123)
coef1 <- rnorm(30)
coef2 <- rnorm(30, mean=2, sd=0.5)
coef3 <- rnorm(30, mean=-2, sd=0.5)
y1 <- data %*% coef1 + rnorm(50)
y2 <- data %*% coef2 + rnorm(50)
y3 <- data %*% coef3 + rnorm(50)
library(caret)
# define cross-validation method
control <- trainControl(method="cv", number=10)
# fit linear regression models and compute CV error
lm1 <- train(y1 ~., data=data, method="lm", trControl=control)
lm2 <- train(y2 ~., data=data, method="lm", trControl=control)
lm3 <- train(y3 ~., data=data, method="lm", trControl=control)
cv_error1 <- lm1$results$RMSE
cv_error2 <- lm2$results$RMSE
cv_error3 <- lm3$results$RMSE
library(glmnet)
library(ggplot2)
# define cross-validation method
cv <- cv.glmnet(x=data, y=y1, alpha=0.5, nfolds=10)
cv_error1 <- cv$cvm
pred_error1 <- sqrt(cv$lambda.min * mean((cv$fit$beta[,cv$lambda == cv$lambda.min] - coef1)^2))
cv <- cv.glmnet(x=data, y=y2, alpha=0.5, nfolds=10)
cv_error2 <- cv$cvm
pred_error2 <- sqrt(cv$lambda.min * mean((cv$fit$beta[,cv$lambda == cv$lambda.min] - coef2)^2))
cv <- cv.glmnet(x=data, y=y3, alpha=0.5, nfolds=10)
cv_error3 <- cv$cvm
pred_error3 <- sqrt(cv$lambda.min * mean((cv$fit$beta[,cv$lambda == cv$lambda.min] - coef3)^2))
# plot CV error
df <- data.frame(Lambda=1:length(cv_error1), CVError1=cv_error1, CVError2=cv_error2, CVError3=cv_error3)
df_melt <- melt(df, id.vars="Lambda", variable.name="Model", value.name="CVError")
ggplot(df_melt, aes(x=Lambda, y=CVError, color=Model)) + geom_line() + ggtitle("CV Error for Three Linear Models")
# plot prediction error
df <- data.frame(Model=c("Model 1", "Model 2", "Model 3"), PredictionError=c(pred_error1, pred_error2, pred_error3))
ggplot(df, aes(x=Model, y=PredictionError)) + geom_bar(stat="identity") + ggtitle("Prediction Error for Three Linear Models")
# calculate upper limit based on one standard deviation criterion
upper_limit <- mean(coef1) + 1*sd(coef1)
```
注意:这里的数据集和系数是随机生成的,每次运行代码结果可能会略有不同。
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