library(olsrr) library(ggplot2) library(gridExtra) library(nortest) library(goftest)

All subset regression tests all possible subsets of the set of potential independent variables. If there are K potential independent variables (besides the constant), then there are $2^{k}$ distinct subsets of them to be tested. For example, if you have 10 candidate independent variables, the number of subsets to be tested is $2^{10}$, which is 1024, and if you have 20 candidate variables, the number is $2^{20}$, which is more than one million.

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars) ols_step_all_possible(model)

The `plot`

method shows the panel of fit criteria for all possible regression methods.

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars) k <- ols_step_all_possible(model) plot(k)

Select the subset of predictors that do the best at meeting some well-defined objective criterion, such as having the largest R2 value or the smallest MSE, Mallow's Cp or AIC.

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars) ols_step_best_subset(model)

The `plot`

method shows the panel of fit criteria for best subset regression methods.

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars) k <- ols_step_best_subset(model) plot(k)

Build regression model from a set of candidate predictor variables by entering predictors based on
p values, in a stepwise manner until there is no variable left to enter any more. The model should include all the candidate predictor variables. If details is set to `TRUE`

, each step is displayed.

# stepwise forward regression model <- lm(y ~ ., data = surgical) ols_step_forward_p(model)

model <- lm(y ~ ., data = surgical) k <- ols_step_forward_p(model) plot(k)

# stepwise forward regression model <- lm(y ~ ., data = surgical) ols_step_forward_p(model, details = TRUE)

Build regression model from a set of candidate predictor variables by removing predictors based on
p values, in a stepwise manner until there is no variable left to remove any more. The model should include all the candidate predictor variables. If details is set to `TRUE`

, each step is displayed.

# stepwise backward regression model <- lm(y ~ ., data = surgical) ols_step_backward_p(model)

model <- lm(y ~ ., data = surgical) k <- ols_step_backward_p(model) plot(k)

# stepwise backward regression model <- lm(y ~ ., data = surgical) ols_step_backward_p(model, details = TRUE)

Build regression model from a set of candidate predictor variables by entering and removing predictors based on
p values, in a stepwise manner until there is no variable left to enter or remove any more. The model should include all the candidate predictor variables. If details is set to `TRUE`

, each step is displayed.

# stepwise regression model <- lm(y ~ ., data = surgical) ols_step_both_p(model)

model <- lm(y ~ ., data = surgical) k <- ols_step_both_p(model) plot(k)

# stepwise regression model <- lm(y ~ ., data = surgical) ols_step_both_p(model, details = TRUE)

Build regression model from a set of candidate predictor variables by entering predictors based on
Akaike Information Criteria, in a stepwise manner until there is no variable left to enter any more.
The model should include all the candidate predictor variables. If details is set to `TRUE`

, each step is displayed.

# stepwise aic forward regression model <- lm(y ~ ., data = surgical) ols_step_forward_aic(model)

model <- lm(y ~ ., data = surgical) k <- ols_step_forward_aic(model) plot(k)

# stepwise aic forward regression model <- lm(y ~ ., data = surgical) ols_step_forward_aic(model, details = TRUE)

Build regression model from a set of candidate predictor variables by removing predictors based on
Akaike Information Criteria, in a stepwise manner until there is no variable left to remove any more.
The model should include all the candidate predictor variables. If details is set to `TRUE`

, each step is displayed.

# stepwise aic backward regression model <- lm(y ~ ., data = surgical) k <- ols_step_backward_aic(model) k

model <- lm(y ~ ., data = surgical) k <- ols_step_backward_aic(model) plot(k)

# stepwise aic backward regression model <- lm(y ~ ., data = surgical) ols_step_backward_aic(model, details = TRUE)

Build regression model from a set of candidate predictor variables by entering and removing predictors based on
Akaike Information Criteria, in a stepwise manner until there is no variable left to enter or remove any more.
The model should include all the candidate predictor variables. If details is set to `TRUE`

, each step is displayed.

# stepwise aic regression model <- lm(y ~ ., data = surgical) ols_step_both_aic(model)

model <- lm(y ~ ., data = surgical) k <- ols_step_both_aic(model) plot(k)

# stepwise aic regression model <- lm(y ~ ., data = surgical) ols_step_both_aic(model, details = TRUE)

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