Final answer:
Multiple regression in R involves predicting a dependent variable using two or more independent variables. The equation includes a y-intercept and slopes for each independent variable. This type of model can be used to analyze significance, fit, and make predictions.
Step-by-step explanation:
An example of multiple regression in R is when you have more than one independent variable predicting the outcome of a dependent variable. This is option 4 from your list. Unlike simple linear regression which has just one independent variable (IV) and one dependent variable (DV), multiple regression can have two or more IVs. The general form of a multiple regression equation is Ŷ = a + b1x1 + b2x2 + ... + bnxn where 'a' represents the y-intercept, b1 through bn are the slopes of the regression equation for each independent variable, and x1 through xn are the independent variables.
For instance, consider a dataset that includes information about students' performance (final grades) based on their hours studied and class attendance. Here, the final grade is the dependent variable while hours studied and class attendance are the independent variables. The R code for performing the multiple regression might look something like this:
model <- lm(final_grade ~ hours_studied + class_attendance, data = student_data)
After fitting this model, you can analyze the significance of the independent variables, the overall fit of the model, and make predictions. The coefficients obtained from the model indicate the change in the dependent variable for one unit of change in an independent variable while holding other variables constant.