# Correlation using Logistic Regression and Pearson

I am so sorry, I am beginner in statistic analysis, I have project using R to analyze the correlation between dependent variables and independents variables.

In this case I have two dependent variables (1. Extrovert, 2. Introvert). And the independent variables i have the data from (Call Log-> how long they call everyday, how many they call everyday, SMS log-> how length text in SMS body every day, how many they sent/received sms for each day).

I am so confused how I can do it, please anyone can give me some good references about it. I also have some questions such as :

1. I use the different type of variables, independent variables (data type : numeric) but dependent variable (data type is categorical), so it is possible to apply logistic regression and Pearson?
2. Or any someone will give me some advice the better solution such as another methods for solving this problem.

The example of data from dput()

structure(list(sumcallin = c(462L, 998L, 335L, 179L, 34L, 0L,
0L, 0L, 0L, 0L), caountcallin = c(7L, 5L, 8L, 5L, 1L, 1L, 0L,
1L, 1L, 1L), sumcallout = c(1068L, 81L, 519L, 393L, 342L, 0L,
583L, 1902L, 358L, 1017L), countcallout = c(15L, 3L, 10L, 5L,
6L, 0L, 3L, 3L, 3L, 3L), sumreceived = c(322L, 75L, 20L, 35L,
8L, 35L, 135L, 103L, 471L, 173L), countreceived = c(15L, 4L,
2L, 3L, 1L, 2L, 7L, 3L, 18L, 5L), sumsent = c(171L, 31L, 25L,
23L, 8L, 55L, 87L, 9L, 400L, 258L), countsent = c(10L, 4L, 1L,
3L, 1L, 3L, 4L, 1L, 13L, 8L), personality = structure(c(2L, 2L,
2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L), .Label = c("extro", "intro"), class = "factor")), .Names = c("sumcallin",
"countreceived", "sumsent", "countsent", "personality"), row.names = c(1L,
2L, 3L, 4L, 5L, 37L, 38L, 39L, 40L, 41L), class = "data.frame")


• From what I understand, 1. Extrovert, 2. Introvert are the two categories that your outcome (dependent) variable can take on. Is that correct? Are you trying to predict whether a new row is Extrovert or Introvert? – Zhubarb Aug 26 '14 at 8:33
• Yes, for the next step, I will, but first time, I just want to know the correlation value for each variables, for example : the incoming call count for every day has positive correlation or negative to the independent variables and I want to know the value. – user46543 Aug 26 '14 at 8:49
• Are you able to post some/all of your data or some representative dummy data? – Zhubarb Aug 26 '14 at 8:51
• Ok, I already adding an example data in my question – user46543 Aug 26 '14 at 9:08

There's a difference between predicting variables and finding out correlation.

Logistic regression is predictor, more specifically, binary classifier. "Classifier" means that it tries to assign some class to every observation. "Binary" means that there are exactly 2 classes. Moreover, logistic regression produces probability with which each observation belongs to each class.

If you want to predict extroversion/introversion, there are 2 options for you:

1. Use each of them as a class and give binary answer. This is simple: person will be assigned either "extrovert" or "introvert" label.
2. Use fuzzy logic. Logistic regression will give you some number between 0 and 1, which represents how much person belongs to specified class. E.g. if you set introversion to 0 and extroversion to 1, and logistic regression return 0.7, then we can say that person is 70% extrovert and 30% introvert. This one is good for capturing things like ambiversion.

Logistic regression works with both - continuous variables and categorical (encoded as dummy variables), so you can directly run logistic regression on your dataset.

Pearson, on other hand, defines correlation. Correlation is simply normalized covariation, and covariation measures how 2 random variables co-variate, that is, how change in one variable is related to change in another one.

Strictly speaking, Pearson correlation cannot deal with categorical variables (mostly because categorical variables don't have a notion of mean, which Pearson is based on). However, having only 2 binary variables you can consider them as continuous (with values of 1 and 0) and calculate a kind of correlation. This is clearly a hack, but it should work for simple explorational analysis.

From your comments, we have clarified that you have a binary outcome (dependent) variable that can take on these values 1. Extrovert, 2. Introvert.

I use the different type of variables, independent variables (data type : numeric) but dependent variable (data type is categorical), so it is possible to apply logistic regression and Pearson?

Yes, since the outcome variable is binary, you can use logistic regression. You can also use Pearson or Spearman or other types of correlations between each independent (predictor) variable and your outcome. Have a read on the different types of correlations and in what scenairos they can be used, here is an example. Also here are some other examples on how to call them in R.

Or can someone give me some advice the better solution such as another methods for solving this problem.

I would start with logistic regression (LR) first, and try to understand what it is doing, look at the coefficents for different variables and their p-values. The task you are eventually trying to accomplish is called binary classification. Apart from LR, there are a lot of different classification algorithms that you can use. But LR is good for a start.

Since it is a classification problem , a binary one to be precise , you could consider decision trees too. I am new to data analysis too , but from all the literature I have been reading you could experiment with couple of models (logistic, decision trees etc) before finalizing the best one.