The anova() function is used for comparing the nested models.

In R, the anova() function is commonly used to perform analysis of variance (ANOVA). ANOVA is a statistical method that is used to analyze the differences among group means in a sample. It is often employed to assess whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

Here’s a brief explanation of the anova() function in R:
anova(model, …)
model: This is typically a linear model object (e.g., created using the lm() function) or an object that can be coerced to a linear model.

…: Additional model objects can be provided, allowing you to compare the fits of different models.

The anova() function compares the fit of different models by performing hypothesis tests. It assesses whether the inclusion of additional terms in a model significantly improves its fit. The output of anova() is an analysis of variance table, which includes the sum of squares, degrees of freedom, mean squares, and F-statistic for each term in the model.

Here’s a simple example using the iris dataset:

# Fit a linear model
model <- lm(Sepal.Length ~ Species, data = iris)

# Perform ANOVA
result <- anova(model)

# Display the ANOVA table
print(result)
In this example, we are using the lm() function to fit a linear model where Sepal.Length is regressed on the variable Species. The anova() function is then applied to test the hypothesis that there are significant differences in the mean sepal length between different species of iris.

The ANOVA table generated by anova() helps you assess the significance of the overall model and the individual terms (in this case, the different species). The F-statistic and p-value are used to make these assessments. A low p-value (typically below a chosen significance level, e.g., 0.05) indicates that there are significant differences between the groups.