I have a dataset that has a binary dependent variable (choose 1=yes, 2=no) and the reasons given to choose each product. Independent variables include color (1=yes, 2=no), flavor (1=yes, 2=no), etc.

Here is a simplified example. I actually have 10 independent variables and n=500.

color flavor choose
1     0      1
1     1      1
1     0      0       

Is it possible to run a binary logistic regression on this dataset? I want to report betas but if possible would like to run Relative Importance of Regressors (R relaimpo package). Any considerations I should have? Is this possible? Should I code the dataset differently?


  • $\begingroup$ If you are interested in any relationship between these variables, a chi-square test would answer this question. It didn't seem clear by your question whether or not you had a clear response variable. What would your outcome variable be for a logistic regression? In other words, if you wanna run a regression, what predictors do you theorize affecting what outcome variable? $\endgroup$ Commented Jan 3, 2023 at 18:02
  • $\begingroup$ choose is the outcome variable either they choose or not the product, and I'm interested ideally on the relative importance of the independent variables $\endgroup$
    – EGM8686
    Commented Jan 3, 2023 at 18:07
  • $\begingroup$ Ah sorry I see now you already mentioned that as a dependent variable. $\endgroup$ Commented Jan 3, 2023 at 18:09
  • 1
    $\begingroup$ @ShawnHemelstrand A standard chi-squared test can be seen as a logistic regression score test. $\endgroup$
    – Dave
    Commented Jan 3, 2023 at 19:08
  • $\begingroup$ Thanks for pointing that out. $\endgroup$ Commented Jan 4, 2023 at 1:09

1 Answer 1


Modeling a binary outcome with binary predictors is fairly standard in logistic regression. Here I have tried to simulate the data you refer to in R and fit it to a logistic regression.

#### Create Fake Data ####
choose <- rbinom(n=500,size=1,prob=.5)
color <- rbinom(n=500,size=1,prob=.5)
flavor <- rbinom(n=500,size=1,prob=.5)
df <- data.frame(choose,color,flavor)

#### Fit Data ####
fit <- glm(
  choose ~ color + flavor,
  data = df,
  family = binomial

If you run summary(fit), you get this readout, which shows you a good amount of information about your model, including the coefficients (which include log odds of each predictor), deviance, AIC, and other info. We can see color has a positive association with the outcome whereas flavor has a negative association:

glm(formula = choose ~ color + flavor, family = binomial, data = df)

Deviance Residuals: 
   Min      1Q  Median      3Q     Max  
-1.145  -1.131  -1.108   1.224   1.248  

            Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.13261    0.15695  -0.845    0.398
color        0.05582    0.17933   0.311    0.756
flavor      -0.03287    0.17924  -0.183    0.854

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 691.35  on 499  degrees of freedom
Residual deviance: 691.22  on 497  degrees of freedom
AIC: 697.22

Number of Fisher Scoring iterations: 3

Probably one of the more important things to obtain is the exponentiated coefficients, which provides odds ratios which may be more useful for interpretation.


This gives us the following readout:

(Intercept)       color      flavor 
  0.8758064   1.0574089   0.9676636 

We can see that color = 1 (whatever that may be, we can call it "red" here) is 1.05 times likely to choose yes (this depends on what your reference value is, here I just say it means yes). Flavor = 1 (perhaps "spicy") slightly decreases the odds of choosing yes.

If you are not experienced on logistic regression or using it within R, a great book on this subject is Practical Guide to Logistic Regression by Joseph Hilbe.


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