Regression with Excel / Multiple Regression with Excel

A guide to regression analysis using MS Excel.

In this section we will describe how to use the Excel™ to carry out some of the procedures we have described in the book. While this approach uses Excel 2003, I don't think that the regression procedure has changed between different versions.

To do regression in Excel, you need the Analysis Toolpak add-in to be installed in Excel. This was an option when you installed Excel, but you might not have selected it. If you didn't install it, Excel will ask you for the CD, when you try to add the toolpak.

Check that the add-in is installed, and added-in, by choosing Add-ins from the tools menu (as shown below).



Then ensure that "Analysis ToolPak" is selected, as shown below.

The Add-Ins Dialog box, in Excel 2000


 

You can now use the data analysis functions in Excel, which include multiple regression.


To get to the data analysis function in Excel, you select the Tools menu, and then choose Data Analysis.

This gives the following Dialog, click on Regression and then click OK.

The Data Analysis Dialog Box in Excel

The following dialog appears:

Regression dialog box, with no details

In here, we tell Excel about the data that we would like to analyse.  
The first box is the input Y range.  Here, we tell Excel about our dependent variable.  The dependent variable must be a column, 1 cell wide, and N cells long (where N is the number of individuals that we are analysing).  
The the dataset we are using, the dependent variable is Anx, which is the column which goes from cell D1 to Cell D41.  You can either type this information in directly as D1:D41, or you can select the appropriate data from the spreadsheet.

Because we have included row 1, which includes the variable name, we are going to have to tell Excel this, by clicking on the "Labels" checkbox.

The next stage is to input the independent variables.  The independent variables must be a block of data, of k columns (where k is the number of independent variables) and N rows (where N is still the number of people).  In the dataset we are using we have three independent variables: hassles, hassles2 and hassles3.  (These represent the linear, quadratic and cubic effects of hassles - we are analysing a non-linear relationship here,)  These are held in rows 1 - 41 of columns A, B and C.  Again, we can type in A1:C41 or select the data from the spreadsheet - it will have the same effect.

Next we tell Excel where we want the results to be written.  It is best to ask for a new sheet - you don't want to accidentally overwrite some of your precious data, and have to go to all of the effort of restoring it from a backup, do you?  (You do have a backup, don't you?)

We can ask fro residuals and standardised residuals to be saved - these will be new columns of numbers created in the the new spreadsheet.


Two types of graphs will be drawn automatically if you ask for them.
  • A residual plot will draw scatter plots of each independent variable on the x-axis, and the residual on the y-axis.
  • A line fit plot will draw scatterplots of each independent variable on the x-axis, and the predicted and actual values of the dependent variable on the y axis.
You cannot, as far as I have been able to determine, automatically have
  • A scatterplot with the predicted values on the x-axis, and the residuals on the y-axis (although you can calculate these values and save them.)
You can also request a normal probability plot. This appears to be a plot of the dependent variable, which is a curious thing to plot - regression analysis does not assume normal distribution of the dependent variable.  The usual plot of this type would be the residuals, but this is not possible in Excel.

The dialog box now looks like this:

The completed dialog box
.
So, finally, we click OK.

And we get a lot of output, written to a new sheet.  A note about this output - output from analysis in Excel is usually "live" that is to say, the data are linked to the output.  If you change the data, you will change the output.  This is not the case for this type of output in Excel.  The results of the analysis are "dead" and will not change.

The Results

The results presented below have been copied from Excel to HTML, so they don't look identical.  You can download the Excel file exactly as Excel wrote it for me here .  Note that the data are not included in this file (it's an Excel 4.0 file, to make it usable by as many people as possible).  
 		  

Regression Statistics
 

Multiple R 0.807582
R Square 0.652189
Adjusted R Square 0.623205
Standard Error 6.686129
Observations 40


 

The first part of the output is the regression statistics.  These are standard statistics which are given by most programs.
 


ANOVA
 

ANOVA
 
 
 
 
 

 		 df SS MS F Significance F
Regression 3 3017.745 1005.915 22.50151 2.22E-08
Residual 36 1609.355 44.70432
 
 
Total 39 4627.1
 
 
 



 

The ANOVA table comes next.  This gives a test of significance of the R2.  Note that Excel uses scientific notation, by default, so when it says 2.22E-08 it means, 2.22 * 10-8 . (i.e. 0.0000000222).  
 


Coefficients
 


 		 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept
12.39
3.90
3.18
0.00
4.48
20.29
4.48
20.29
HASSLES
-0.06
0.34
-0.19
0.85
-0.75
0.62
-0.75
0.62
HASSLES2
0.00
0.01
0.06
0.95
-0.02
0.02
-0.02
0.02
HASSLES3
0.00
0.00
0.51
0.61
0.00
0.00
0.00
0.00


 

The next stage is the coefficients.  Note that here I have converted the numbers to 2 decimal places to save space).   It gives the coefficient for each parameter, including the intercept (the constant).  The standard errors, and the t-values follow (the t-value is the coefficient divided by the standard error).  Next comes the p-value associated with the variable, and the confidence intervals of the parameter estimates (Excel gave these to me twice, even though I didn't ask for them.)
 


Residuals
 

Observation
Predicted ANX
Residuals
Standard Residuals
1.00
12.08
-2.08
-0.32
2.00
11.82
0.18
0.03
3.00
15.98
5.02
0.78
4.00
29.86
-13.86
-2.16
5.00
28.56
-1.56
-0.24
6.00
34.16
-4.16
-0.65
7.00
12.32
-3.32
-0.52
8.00
12.37
-5.37
-0.84
9.00
27.31
4.69
0.73
10.00
15.64
-4.64
-0.72


 

The final part of the output is the residual information.  The observation in the left had column is the case number - although Excel never told us about this, it has labelled the first person Observation  1, the second Observation  2, etc.  (Note that this is NOT the original row number - Observation 1 was row 2).  
The predicted anxiety score is the score that was predicted from the regression equation.  The residual is the raw residual - that is the difference between the predicted score and the actual score on the dependent variable. The final value is the standardised residual (the residuals adjusted to ensure that they have a standard deviation of 1; they have a mean of zero already).

 
Graphs

Finally we will have a quick look at the graphs.

The first graph is an example of the residual plots - it has hassles on the x-axis and the unstandardised residual on the y-axis.

Plot of hassles against residuals

The second graphs shows the predicted and actual anxiety scores plotted against hassles3.

Plot of Hassles3 against predicted and actual anxiety scores


 



 

A Note to End On
I have written this file which shows you how to do regression in Excel, but this does not mean that I think that you should be doing regression in Excel.   Regression in Excel has a number of shortcomings, which include:
  • No standardised coefficients.  It  can be very difficult to interpret unstandardised coefficients.  You could calculate the standardised coefficients using the unstandardised coefficients, if you really wanted to.  But you could have done the regression on your own, if you really wanted to.
  • Lack of diagnostic graphs.  The standard diagnostic graphs are not available in Excel, e.g. the normality plot of the residuals, the scatterplot or residuals against predicted values.  Again, you can work them out, but it ain't easy.
  • Lack of Diagnostic statistics.  There are no collinearity diagnostics, which would help you to understand what was happening in the data that we analysed above (highly significant R2, but no significant parameters in the model).   You could calculate the skew statistics, but not if you have more than 30 cases.
  • Lack of features.  There is no hierarchical regression, no weighting cases,  etc, etc, etc...
  • Inflexibility.  If you want to run a slightly different analysis, it is hard work, because you have to move your data around, a process which is prone to errors.