Simple Linear Regression & Applications

Linear Regression – Template for Student Use

Part 1: Introduction

State the relationship to be explored. This should include a thorough discussion of the two variables and how they are likely to be related. Explain for the layman the intuitive relationship between the two variables. 

Part 2: The Data 

Give an overview of the data. For small data sets the data can be put in a table, for large data sets the data should have a descriptive table with mean, range, defining variable names for use in regression etc.

If you use variable names this is the place to define them…they can be defined in the table of summary statistics if that suits you. Notice that in the next section you will have to produce the regression equation and it will look much clearer if you don’t have variables which are several words or very long strings of letters.

Part 3: Regression Results

You should first describe the regression you are going to perform.  The results of the regression should be shown in equation form. 

You should then interpret the regression results. This includes describing precisely what the coefficients on the independent variable(s) is (are) and explain how the changes in these variables are related to changes in the dependent variable. Include also a short discussion on the intercept term and its interpretation.

Lastly, you should note if the results seem reasonable if possible. 

Part 4: The sufficient conditions for good estimates

Linear in parameters

Here you should show scatter plots of the independent variable(s) versus the dependent variable and comment if it looks like there is a linear relationship between the two.  If there is no linear relationship between the variables then note this as a weakness of the analysis.  

Random sampling

In this section you are to discuss how the data was collected and if there is any reason to believe that the data is not representative of the population you are studying. 

Variation in the independent variable(s)

Discuss if there are any gaps in the independent variables that might make it difficult to extrapolate from the data to an estimate. Is there enough variation in the independent variables in relation to the dependent variable? (It might be good to refer to the data summary (part 2) or the scatter plots created above.)

Zero mean of the error term conditional on the independent variable(s)

For this the obvious thing to think about is everything else that can affect the dependent variable that you have not included as an independent variable in your regression and opine on if these things are likely to be correlated with any of your independent variables which are included in the regression analysis. 

This material was created by Dr. Curtis R. Price for the purposes of instruction. All rights are reserved by the author.