A dummy variable is a type of variable that we create in regression analysis so that we can represent a categorical variable as a numerical variable that takes on one of two values: zero or one.

For example, suppose we have the following dataset and we would like to use *age* and *marital status *to predict *income*:

To use *marital status* as a predictor variable in a regression model, we must convert it into a dummy variable.

Since it is currently a categorical variable that can take on three different values (“Single”, “Married”, or “Divorced”), we need to create *k*-1 = 3-1 = 2 dummy variables.

To create this dummy variable, we can let “Single” be our baseline value since it occurs most often. Thus, here’s how we would convert *marital status* into dummy variables:

This tutorial provides a step-by-step example of how to create dummy variables for this exact dataset in R and then perform regression analysis using these dummy variables as predictors.

**Step 1: Create the Data**

First, let’s create the dataset in R:

#create data frame df <- data.frame(income=c(45000, 48000, 54000, 57000, 65000, 69000, 78000, 83000, 98000, 104000, 107000), age=c(23, 25, 24, 29, 38, 36, 40, 59, 56, 64, 53), status=c('Single', 'Single', 'Single', 'Single', 'Married', 'Single', 'Married', 'Divorced', 'Divorced', 'Married', 'Married')) #view data frame df income age status 1 45000 23 Single 2 48000 25 Single 3 54000 24 Single 4 57000 29 Single 5 65000 38 Married 6 69000 36 Single 7 78000 40 Married 8 83000 59 Divorced 9 98000 56 Divorced 10 104000 64 Married 11 107000 53 Married

**Step 2: Create the Dummy Variables**

Next, we can use the **ifelse()** function in R to define dummy variables and then define the final data frame we’d like to use to build the regression model:

#create dummy variables married <- ifelse(df$status == 'Married', 1, 0) divorced <- ifelse(df$status == 'Divorced', 1, 0) #create data frame to use for regression df_reg <- data.frame(income = df$income, age = df$age, married = married, divorced = divorced) #view data frame df_reg income age married divorced 1 45000 23 0 0 2 48000 25 0 0 3 54000 24 0 0 4 57000 29 0 0 5 65000 38 1 0 6 69000 36 0 0 7 78000 40 1 0 8 83000 59 0 1 9 98000 56 0 1 10 104000 64 1 0 11 107000 53 1 0

**Step 3: Perform Linear Regression**

Lastly, we can use the **lm()** function to fit a multiple linear regression model:

#create regression model model <- lm(income ~ age + married + divorced, data=df_reg) #view regression model output summary(model) Call: lm(formula = income ~ age + married + divorced, data = df_reg) Residuals: Min 1Q Median 3Q Max -9707.5 -5033.8 45.3 3390.4 12245.4 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 14276.1 10411.5 1.371 0.21266 age 1471.7 354.4 4.152 0.00428 ** married 2479.7 9431.3 0.263 0.80018 divorced -8397.4 12771.4 -0.658 0.53187 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 8391 on 7 degrees of freedom Multiple R-squared: 0.9008, Adjusted R-squared: 0.8584 F-statistic: 21.2 on 3 and 7 DF, p-value: 0.0006865

The fitted regression line turns out to be:

Income = 14,276.1 + 1,471.7*(age) + 2,479.7*(married) – 8,397.4*(divorced)

We can use this equation to find the estimated income for an individual based on their age and marital status. For example, an individual who is 35 years old and married is estimated to have an income of **$68,264**:

Income = 14,276.2 + 1,471.7*(35) + 2,479.7*(1) – 8,397.4*(0) = $68,264

Here is how to interpret the regression coefficients from the table:

**Intercept:**The intercept represents the average income for a single individual who is zero years old. Obviously you can’t be zero years old, so it doesn’t make sense to interpret the intercept by itself in this particular regression model.**Age:**Each one year increase in age is associated with an average increase of $1,471.70 in income. Since the p-value (.004) is less than .05, age is a statistically significant predictor of income.**Married:**A married individual, on average, earns $2,479.70 more than a single individual. Since the p-value (0.800) is not less than .05, this difference is not statistically significant.**Divorced:**A divorced individual, on average, earns $8,397.40 less than a single individual. Since the p-value (0.532) is not less than .05, this difference is not statistically significant.

Since both dummy variables were not statistically significant, we could drop *marital status* as a predictor from the model because it doesn’t appear to add any predictive value for income.