# Multiple Linear Regression

Statistics Solutions provides a data analysis plan template for the multiple linear regression analysis.  You can use this template to develop the data analysis section of your dissertation or research proposal.

The template includes research questions stated in statistical language, analysis justification and assumptions of the analysis.  Simply edit the blue text to reflect your research information and you will have the data analysis plan for your dissertation or research proposal.

Data Analysis Plan: Multiple Linear Regression

Copy and paste the following into a word document to use as your data analysis plan template.  *This analysis will have any number of independent variables

Research Question:

RQ: Do independent variable 1independent variable 2, and independent variable 3 predict dependent variable?

HoIndependent variable 1, independent variable 2, and independent variable 3 do not predict dependent variable.

Ha: Independent variable 1independent variable 2, and independent variable 3 predict dependent variable.

Data Analysis

To examine the research question, a multiple linear regression will be conducted to assess if the independent variables predict the dependent variable (criterion).  A multiple linear regression assesses the relationship among a set of dichotomous, or ordinal, or interval/ratio predictor variables on an interval/ratio criterion variable.  In this instance, the independent variables include independent variable 1independent variable 2, and independent variable 3 and the dependent variable is dependent variable.  The following regression equation (main effects model) will be used: y = b1*x1 + b2*x2 +b3*x3+…+ c; where Y = estimated dependent variable, c = constant (which includes the error term), b = regression coefficients and x = each independent variables.

Standard multiple linear regression—the enter method—will be used.  The standard method enters all independent variables (predictors) simultaneously into the model.  Unless theory sufficiently supports a different method, enter is standard method of variable entry.  Variables will be evaluated by what they add to the prediction of the dependent variable which is different from the predictability afforded by the other predictors in the model.  The F-test will be used to assess whether the set of independent variables collectively predicts the dependent variable.  R-squared—the multiple correlation coefficient of determination—will be reported and used to determine how much variance in the dependent variable can be accounted for by the set of independent variables.  The t test will be used to determine the significance of each predictor and beta coefficients will be used to determine the magnitude of prediction for each independent variable.  For significant predictors, every one unit increase in the predictor, the dependent variable will increase or decrease by the number of unstandardized beta coefficients.

The assumptions of multiple regression—linearity, homoscedasticity and multicollinearity—will be assessed.  Linearity assumes a straight line relationship between the predictor variables and the criterion variable, and homoscedasticity assumes that scores are normally distributed about the regression line.  Linearity and homoscedasticity will be assessed by examination of a scatter plot.  The absence of multicollinearity assumes that predictor variables are not too related and will be assessed using Variance Inflation Factors (VIF).  VIF values over 10 will suggest the presence of multicollinearity.

Reference