Excel Regression Tutorial

Before you can perform a linear regression with Excel, you need to make sure the "add-in" is installed.
In Excel, click on tools and Add-ins, a window will open that looks like this:

Make sure the "Analysis Tookpak" box is checked, then click OK.

A linear regression is just a statistical tool used to determine whether or not two (or more) variables are linearly related. 

Suppose you want to determine whether a person's salary is a function of his or her education level (measured in years).
The general form of the relationship is:

Y_i = a + bX_i + error_i

where:

• Y_i = value of Y (salary) for observation i
• a  = average value of Y (salary) when X (education) is zero
• b = average change in Y (salary) given a one unit increase in X (education), i.e. the average increase in salary for each    additional year of eduction
• X_i = value of X (education) for observation i
• error_i = portion of Y (salary) that is unrelated to X (education), i.e. due to other factors (age, years on job, etc.)

You start by collecting a random sample of  observations, and recording them in your spreadsheet.  For ease of computation, it helps to put the dependent varialble (Y) in the left column, and the independent variable (X) in the right column.

Click on "Tools" and then "Data Analysis" and a window like this will appear:

Scroll down until you see the "Regression" tool, click on it, then click OK.

You will see a box like this:

Click inside the box labeled "Input Y Range:" and then click on cell B1 and hold the left mouse button down and highlight cells B1 throught B14

Next, click inside the box labeled "Input X Range:" and then click on cell C1 and hold the left mouse button down and highlight cells C1 throught C14

Since we have labels at the top of each data column (and included their cells in the ranges above) click the "Labels" checkbox and then click the "Line Fit Plots" checkbox. 

Now, click OK and Excel will perform the linear regression, and put the output on a new page:

Cell B17 contains the "intercept" i.e. the value of "a" from the equation: Y_i = a + bX_i + error_i

Cell B18 contains the slope, i.e. the value of "b" from the equation: Y_i = a + bX_i + error_i

So, our regression equation is:    Salary = 12,226 + 1833(Education)
We interpret it as: on average, a person's salary is $12,226 plus $1,833 each year of education he/she has.

We should also look at the "Adjusted R Square" statistic in cell B6 to determine how strong the relationship between salary and education is.  In this case, its value is 0.60, which indicates that about 60% of  salary is determined by education (so about 40% is determined by other factors).

We can also look at the line fit plot to get a visual feel for how "linear" the relationship is:

The pink squares show the "predicted" relationship, i.e. a perfectly straight line from the equation: Y_i = a + bX_i 

The dark blue diamonds show the actual relationship: Y_i = a + bX_i + error_i
The error term accounts for the fact that the part of salary is due to other factors not included in our model.