Computing p-value from F-statistic for a regression model
Consider that we have a dataset that shows the total distance traveled, total emission generated, mileage obtained at the end:
R
# Create a dataset dataset <- data.frame(distance = c(112, 217, 92, 98, 104), emission = c(4.5, 9.8, 12.1, 3.2, 7.6), mileage = c(15, 12, 16, 19, 21)) # Display the dataset dataset |
Output:
Now, we can fit a linear regression model to this data using distance and mileage as the predictor variables and mileage as the response variable. To fit a regression model, R provides us lm() using which we can fit the linear regression model easily. It has the following syntax:
Syntax: lm( formula, dataframe )
Parameters:
- formula: It represents the formula for the linear model.
- dataframe: It represents a data frame that contains the data.
To print the summary of the linear model, we can use the summary() function. This function has the following syntax:
Syntax: summary(model)
Parameters: model: It represents a model
The complete source code is given below:
R
# Create a dataset dataset <- data.frame(distance = c(112, 217, 92, 98, 104), emission = c(4.5, 9.8, 12.1, 3.2, 7.6), mileage = c(15, 12, 16, 19, 21)) # Fit a regression model model <- lm(mileage ~ distance + emission, data = dataset) # Display the output of the model summary(model) |
Output:
The F-statistic for the overall regression model comes out to be equal to 1.321. This F-statistic has 2 degrees of freedom for the numerator as well as for the denominator. The p-value for this F-statistic is equal to 0.4309.
We can calculate this equivalent p-value with the help of the following code:
R
# Compute the p-value pf(1.321, 2, 2, lower.tail = FALSE) |
Output:
As you can see in the output, we got an almost similar result.
How to Calculate the P-Value of an F-Statistic in R
F-test is a statistical test and it produces the F-statistic which possesses F distribution under the null hypothesis. This article focuses on how we can compute the P-value of an F-statistic in R Programming Language.