Many times, multiple variables can be correlated, affecting the outcome of the
dependent variable. Describe, in detail, the process for determining if more
than one variable contributes to the outcome of a single dependent variable.
This relates to Multiple Linear Regression. Multiple variables affecting the dependent variable can be
correlated. This is known by multi-collinearity.
One can use stepwise regression to conclude that if more than one variable contributes to outcome
of a single dependent variable or not. In stepwise regression (both direction), we start with no
variable in the model. Then fit the regression model on each independent variable and see which
one is most significant. And again carry on the procedure. This will give the significant variables
affecting the dependent variable and problem of multi-collinearity will also get reduced
To analyze the relationship between multiple variables and a single dependent variable, we can
use multiple linear regression analysis. In multiple linear regression analysis, multiple predictor
variables can be correlated with the dependent variable. We can use stepwise regression analysis
to find out if one or multiple predictor variables contribute to the outcome variable. In stepwise
regression analysis, the decisions about the order in which predictors enter the model is based on
purely mathematical criterion. Firstly, use forward method that is the initial model contains only
the constant. Then the computer searches for the predictor that best predicts the outcome variable
according to the highest simple correlation.
How accurate is a regression analysis and how do you know? What attributes of the analysis
will determine whether the analysis is accurate and to what extent? Can inaccurate
regression analyses be used to an analyzer’s benefit? Explain in detail.
Regression analysis is to use a linear model as a way to predict values of a dependent variable
from a set of independent variables. In simple regression analysis, we can use the value of R
square to determine the accuracy of the model. R square can range from 0 to 1. The model will
be a good fit if R square is close to 1; on the other hand, the model will not be a good fit if R
square is close to 0. In multiple regression analysis, we can use adjusted R square to test the
accuracy of the model. Same with R square, adjusted R square also ranges from 0 to 1, with 1
indicating better fit of the model. If the regression analysis is not accurate. It should not be used
for outcome prediction of variables since it will not give an accurate measurement. It will give a
misleading result.
