REGRESSION ANALYSIS-R

Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In R, the most commonly used package for regression analysis is lm() (linear model) which is part of the base R installation. Another popular package is glm() (generalized linear model) which is also part of the base R installation. Both of these functions can be used to perform a variety of regression analyses including simple linear regression, multiple linear regression, and logistic regression. Additionally, there are several specialized packages in R such as lme4 and nlme that can be used to perform more advanced types of regression analysis such as mixed-effects and non-linear models.

Here is an example of how to perform a simple linear regression using the lm() function and visualize the results using the ggplot2 package in R:

library(ggplot2)

generate some example data

x <- rnorm(100, mean = 10, sd = 2)

y <- x + rnorm(100, mean = 0, sd = 2)

perform linear regression

The lm() function in R is used to fit a linear model to a set of data. In this case, the function is being used to fit a simple linear regression model, where the dependent variable is y and the independent variable is x. The formula passed to the function, y ~ x, describes the relationship between the two variables.

The ~ symbol is used to separate the dependent variable (on the left-hand side of the ~) from the independent variable(s) (on the right-hand side of the ~). In this case, y is the dependent variable, and x is the independent variable.

The result of this function call is an object of class "lm" that contains information about the fitted model, such as the coefficients, residuals, and other statistics.

The general syntax of the function is:

lm(formula, data, subset, weights, na.action, ...)

• formula: A formula specifying the model. The left-hand side of the formula should be the response variable and the right-hand side should be the predictor variable(s).
• data: The data frame containing the variables in the formula.
• subset: An optional vector specifying a subset of observations to be used in the fitting process.
• weights: An optional vector of weights to be used in the fitting process.
• na.action: A function which indicates what should happen when the data contains missing values.
• ...: Additional arguments to be passed to the low-level functions.

This is a simple example but in practice, the data and the formula can be more complex. The lm() function can also be used to fit multiple linear regression models, where the dependent variable is related to multiple independent variables.

fit <- lm(y ~ x)

create a scatter plot of the data and the regression line

ggplot(data = data.frame(x, y), aes(x = x, y = y)) +

  geom_point() +

  geom_smooth(method = "lm", se = T)

Here is an example of how to perform a simple linear regression using the lm() function with a real dataset and visualize the results using the ggplot2 package in R:

# load the mtcars dataset data(mtcars) # perform linear regression fit <- lm(mpg ~ hp, data = mtcars) # create a scatter plot of the data and the regression line ggplot(data = mtcars, aes(x = hp, y = mpg)) + geom_point() + geom_smooth(method = "lm", se = FALSE)

Multiple linear regression:

# generate example data x1 <- rnorm(100, mean = 10, sd = 2) x2 <- rnorm(100, mean = 10, sd = 2) y <- x1 + x2 + rnorm(100, mean = 0, sd = 2) # perform multiple linear regression fit <- lm(y ~ x1 + x2) # visualize the results library(stargazer) stargazer(fit, type = "text", out = "regression_results.txt")

This will create an text file with the regression results, including the coefficients, p-values, and R-squared value for the model, using the variables wt, hp, and drat as independent variables and mpg as dependent variable.

# perform multiple linear regression fit <- lm(mpg ~ wt + hp + drat, data = mtcars) # visualize the results

The stargazer function is a package for R that creates beautiful LaTeX or ASCII tables of regression models, data frames, and other statistical objects. The first argument, fit, is the object to be summarized (e.g. a regression model). The type argument specifies the format of the output, and can be set to "text" to output the table as plain text. The out argument specifies the file name to which the table will be written. In this case, the table will be written to a file named "regression_results.txt" in the current working directory.

library(stargazer) stargazer(fit, type = "text", out = "regression_results.txt")