Dummy Variable Regression Excel

[Vinay Pettyjohn]

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 am transitioning from Stata to R. In Stata, if I label a factor levels (say--0 and 1) to (M and F), 0 and 1 would remain as they are. Moreover, this is required for dummy-variable linear regression in most software including Excel and SPSS.

However, I've noticed that R defaults factor levels to 1,2 instead of 0,1. I don't know why R does this although regression internally (and correctly) assumes 0 and 1 as the factor variable. I would appreciate any help.

I did check other threads on SO, but they mostly talk about how R codes factor variables without telling me why. Stata and SPSS generally require the base variable to be "0." So, I thought of asking about this.

R is not Stata. And you will need to unlearn a lot of what you have been taught about dummy variable construction. R does it behind the scenes for you. You cannot make R behave exactly as Stata. True, R did have 0's and 1' in the model matrix column for the "F" level but those get multiplied by the factor values, (1 and 2 in this case). However, contrasts are always about differences and the difference btwn (0,1) is the same as the difference btwn (1,2).

What you see from str() is the internal representation of a factor variable. A factor is internally an integer, where the number gives the position of levels inside the vector. For example:

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.

In this section, we work through a simple example to illustrate the use of dummy variables in regression analysis. The example begins with two independent variables - one quantitative and one categorical. Notice that once the categorical variable is expressed in dummy form, the analysis proceeds in routine fashion. The dummy variable is treated just like any other quantitative variable.

The first thing we need to do is to express gender as one or more dummy variables. How many dummy variables will we need to fully capture all of the information inherent in the categorical variable Gender? To answer that question, we look at the number of values (k) Gender can assume. We will need k - 1 dummy variables to represent Gender. Since Gender can assume two values (male or female), we will only need one dummy variable to represent Gender.

Note that X1 identifies male students explicitly. Non-male students are the reference group. This was a arbitrary choice. The analysis works just as well if you use X1 to identify female students and make non-female students the reference group.

At this point, we conduct a routine regression analysis. No special tweaks are required to handle the dummy variable. So, we begin by specifying our regression equation. For this problem, the equation is:

Values for IQ and X1 are known inputs from the data table. The only unknowns on the right side of the equation are the regression coefficients, which we will estimate through least-squares regression.

The first task in our analysis is to assign values to coefficients in our regression equation. Excel does all the hard work behind the scenes, and displays the result in a regression coefficients table:

The coefficient of muliple determination is 0.810. For our sample problem, this means 81% of test score variation can be explained by IQ and by gender. Translation: Our equation fits the data pretty well.

Before we conduct those tests, however, we need to assess multicollinearity between independent variables. If multicollinearity is high, significance tests on regression coefficient can be misleading. But if multicollinearity is low, the same tests can be informative.

To measure multicollinearity for this problem, we can try to predict IQ based on Gender. That is, we regress IQ against Gender. The resulting coefficient of multiple determination (R2k) is an indicator of multicollinearity. When R2k is greater than 0.75, multicollinearity is a problem.

With multiple regression, there is more than one independent variable; so it is natural to ask whether a particular independent variable contributes significantly to the regression after effects of other variables are taken into account. The answer to this question can be found in the regression coefficients table:

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