Question

1. Which of the following is a false statement?

   	A.	In a multiple regression model, adding more explanatory variables to the model is always a good idea because R2 always increases as more explanatory variables are added to the model.
   	B.	In a multiple regression model, the explanatory variables, or X variables, are often correlated.
   	C.	In a multiple regression model, the goals are to describe the relationship between Y and two or more X variables and to predict the value of Y using two or more X variables.
   	D.	In a multiple regression model, interactions can occur between the X variables.

Answer 1

Option A

R2 value in a regression analysis gives us the percentage of variability in dependent variable that is explained by the independet variables.

So, if we add more independent variables or explanatory variables, the explained variance previously without the new variables won't decrease after adding new variables because the model will have option to ignore the new variable and work with the variables we already have.

So the R2 value will always increase with addition of new explanatory variables.

So option A is True

Option C

The main aim or goal of a multiple regression modei is to describe the relationship between the dependent variable Y and two or more independent variables X and then predict the value of Y with known values of X

So Option C is True

Option D

In a multiple regression model, interaction can occur between the X variables when the effect of an X variable or indpependent variable on an Y variable or dependent variable changes, based on the values of one or more X variables or independent variables.

So interaction can occur between the independent variables

So Option D is True

Option B

The independent variables in a multiple regression model should be independent of each other. When there is a correlation between the independent variables, they will create a problem when we model the regression and try to find out or predict the y-values and then interpret the results. So in ost of the models, if two X variables or independent variables have high corelation between them, we drop one of the variables while building our regression model

So the explanatory variables, or X variables, are often correlated.is False, they will have corelation rarely

So Option B is False

So Answer is Option B