Dummy Variables In Regression Excel

[Nico Sadiq]

Yourquestion is stale now. Excel definitely can solve regression problems with dummy variables, although it is some time since I did it. I have not tried with Solver, but would be surprised if one of the solver engines can not do it. Once you have set up your equations, start Solver and select the options button. There are a number of engines that you can select from as well as other parameters you can try.

Newbie question here: I'm doing dummy variable regression using JMP for a school project. When I cross-referenced to Excel's version, I realized the coefficients are completely different even though the t-stats are the same.

1) I can't seem to find the standard error of estimate for the overall model after running the regression (I can find only the standard error for each independent variable). Can you point me in the right direction for this?

2) Let's say I've coefficient estimates generated from one regression, and those generated from another regression. Am I able to run a t-test of the coefficient estimates in JMP? If so, do you have any advice how I can approach that?

Hi Mark,

Thanks for getting back so promptly.

If you refer to the attached images, that's the analysis output after running a regression. So my question is, is there a way for me to find the "total standard error of estimate", if there's such a thing since currently all I can see about the standard error is of each coefficient estimate.

Thanks. I understand where you're coming from.

Another thing is, is there a way to find the standard error of beta coefficient for each independent variable in the Fit Model's Analysis? I understand this is the method used to find beta coefficient:

Creating a dummy variable in Excel is a fundamental data processing task, essential for statistical analysis and modeling. This guide provides step-by-step instructions on how to efficiently transform categorical data into numerical format required for many analytical procedures.

Understanding the nuances of dummy variable creation can streamline data prep activities. However, we'll also explore why using a platform like Sourcetable can simplify this process even more than traditional Excel methods.

Excel's IF() function is the primary tool for creating dummy variables. This function assigns a value of 1 or 0 based on a specified condition, effectively converting categorical data into a binary numerical format suitable for regression models.

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I imagine there's a strong correlation between time and distance and probably a weaker one to engine size (and none to shoe size). Presumably multiple regression analysis / ANOVA is the tool to use. But how do I include day of week, since just coding it as Sunday=1, Monday=2 etc feels very wrong?

Having used Excel's regression tool, for example, how do I interpret the results? Presumably if R is close to 1 this is good (although if there are many data items it seems as though it can be small yet still be significant). But some sources refer to r-squared which seems to be the SD, so a value close to zero is good. It also shows the t Stat, P-value, F and Significance F, whatever they may be. Can anyone recommend a good reference source?

What you need is a solid review of regression methodology. However, these questions are sufficiently basic (don't take that the wrong way) that even a good overview of basic statistics would probably benefit you. Howell has written a very popular textbook that provides a broad conceptual foundation without requiring dense mathematics. It may well be worth your time to read it. It is not possible to cover all of that material here. However, I can try to get you started on some of your specific questions.

First, days of the week are included via a coding scheme. The most popular is 'reference category' coding (typically called dummy coding). Lets imagine that your data are represented in a matrix, with your cases in rows and your variables in columns. In this scheme, if you had 7 categorical variables (e.g., for days of the week) you would add 6 new columns. You would pick one day as the reference category, generally the one that is thought of as the default. Often this is informed by theory, context, or the research question. I have no idea which would be best for days of the week, but it also doesn't really matter much, you could just pick any old one. Once you have the reference category, you could assign the others to your new 6 variables, then you simply indicate whether that variable obtains for each case. For example, say you pick Sunday as the reference category, your new columns / variables would be Monday-Saturday. Every observation that took place on a Monday would be indicated with a $1$ in the Monday column, and a $0$ elsewhere. The same would happen with observations on Tuesdays and so on. Note that no case can get a $1$ in 2 or more columns, and that observations that took place on Sunday (the reference category) would have $0$'s in all of your new variables. There are many other coding schemes possible, and the link does a good job of introducing them. You can test to see if the day of the week matters by testing the nested model with all of the new 6 variables dropped vs. the full model with all 6 included. Note that you should not use the tests that are reported with standard output, as these are not independent and have intrinsic multiple comparison problems.

It has been a long time since I've looked at how Excel does statistics, and I don't remember it very clearly, so someone else may be able to help you more there. This page seems to have some information about the specifics of regression in Excel. I can tell you a little more about the statistics typically reported in regression output:

One last point that's worth emphasizing is that this process cannot be divorced from its context. To do a good job of analyzing data, you must keep your background knowledge and the research question in mind. I alluded to this above regarding the choice of the reference category. For example, you note that shoe size should not be relevant, but for the Flintstones it probably was! I just want to include this fact, because it often seems to be forgotten.

You end with lots of questions which requires "teaching" regression. Let me say that higher R^2 is better but there are caveats. R^2 always goes up as you add variables so you can artificially inflate it. Look at significance tests, look at residual diagnostics, etc. With respect to day of the week, Monday = 1, Tuesday = 2, etc. would not be the way to go. What you want are seasonal indicator variables: 0/1 if Monday, 0/1 if Tuesday, etc.

Technically, dummy variables are dichotomous, quantitative variables. Their range of values is small; they can take on only two quantitative values. As a practical matter, regression results are easiest to interpret when dummy variables are limited to two specific values, 1 or 0. Typically, 1 represents the presence of a qualitative attribute, and 0 represents the absence.

The number of dummy variables required to represent a particular categorical variable depends on the number of values that the categorical variable can assume. To represent a categorical variable that can assume k different values, a researcher would need to define k - 1 dummy variables.

For example, suppose we are interested in political affiliation, a categorical variable that might assume three values - Republican, Democrat, or Independent. We could represent political affiliation with two dummy variables:

In this example, notice that we don't have to create a dummy variable to represent the "Independent" category of political affiliation. If X1 equals zero and X2 equals zero, we know the voter is neither Republican nor Democrat. Therefore, voter must be Independent.

When defining dummy variables, a common mistake is to define too many variables. If a categorical variable can take on k values, it is tempting to define k dummy variables. Resist this urge. Remember, you only need k - 1 dummy variables.

A kth dummy variable is redundant; it carries no new information. And it creates a severe multicollinearity problem for the analysis. Using k dummy variables when only k - 1 dummy variables are required is known as the dummy variable trap. Avoid this trap!

The value of the categorical variable that is not represented explicitly by a dummy variable is called the reference group. In this example, the reference group consists of Independent voters.

In analysis, each dummy variable is compared with the reference group. In this example, a positive regression coefficient means that income is higher for the dummy variable political affiliation than for the reference group; a negative regression coefficient means that income is lower. If the regression coefficient is statistically significant, the income discrepancy with the reference group is also statistically significant.

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