Data Preparation

Logistic regression is used to model the probability of a perticular class or event existing binary outputs such as pass/fail, win/lose, alive/dead, or healthy/sick. Logistic regression uses a logistic function to model a binary dependent variable.

1. Functionalities

  • To upload data files, preview data set, and check the correctness of data input
  • To pre-process some variables (when necessary) for building the model
  • To achieve the basic descriptive statistics and draw plots of the variables

2. About your data (training set)

  • Your data need to include one binary dependent variable (denoted as Y) and at least one independent variables (denoted as X)
  • Your data need to have more rows than columns
  • Do not mix character and numbers in the same column
  • The data used to build a model is called a training set

Case Example

Suppose we wanted to explore the Breast Cancer dataset and develop a model to try classifying suspected cells to Benign (B) or Malignant (M). The dependent variable is a binary outcome (B/M). We were interested in (1) building a model to calculate the probability of benign or malignant, and to determine whether the patient is benign or malignant, and (2) finding out the relations between the binary dependent variable and the other variables, that is finding out which variable contributes significantly to the dependent variable.

Please follow the Steps, and Outputs will give real-time analytical results. After getting data ready, please find the model in the next tabs.


Training Set Preparation




Upload data will cover the example data

Please refer to the example data format to upload new data

2. Show 1st row as column names?

3. Use 1st column as row names? (No duplicates)

Correct separator and quote ensure the successful data input

Find some example data here

Change the types of some variable?

Change the referential level for categorical variable?

2. Input the referential level, each line for one variable






Output 1. Data Information

Data Preview

Variable types


Output 2. Descriptive Results


1. For numeric variable

2. For categorical variable


Logit plot: to roughly show the relation between any two numeric variable.


3. Change the labels of X and Y axes


Histogram: to roughly show the probability distribution of a variable by depicting the frequencies of observations occurring in certain ranges of values.

Density plot: to show the distribution of a variable


Histogram

When the number of bins is 0, plot will use the default number of bins

Density plot


Logistic Regression

1. Functionalities

  • To build simple or multiple logistic regression model
  • To achieve the estimates of regressions, including (1) estimate of coefficients with t test, p value, and 95% CI, (2) R2 and adjusted R2, and (3) F-Test for overall significance in Regression
  • To achieve additional information: (1) predicted dependent variable and residuals, (2) AIC-based variable selection, (3) ROC plot, and (4) sensitivity and specificity table for ROC plot
  • To upload new data and achieve the prediction
  • To achieve the evaluation of new data containing new dependent variable

2. About your data

  • The dependent variable is binary
  • Please prepare the training set data in the previous Data tab
  • New data (test set) should cover all the independent variables used in the model.

Please follow the Steps to build the model, and click Outputs to get analytical results.


Prepare the Model

Prepare the data in the previous tab


Step 1. Choose variables to build the model


Step 2. Check the model

Valid model example: Y ~ X1 + X2

              

'-1' in the formula indicates that intercept / constant term has been removed


Step 3. If data and model are ready, click the blue button to generate model results.





Output 1. Data Preview



                

Check full data in Data tab


Output 2. Model Results



Explanations
  • Output in the left shows estimated coefficients (95% confidence interval), T statistic (t = ) for the significance of single variable, and P value (p = ) are given
  • Output in the right shows odds ratio = exp(b) and standard error of the original coefficients
  • T test of each variable and P < 0.05 indicates this variable is statistically significant to the model
  • Observations mean the number of samples
  • Akaike Inf. Crit. = AIC = -2 (log likelihood) + 2k; k is the number of variables + constant


Explanations
  • The Akaike Information Criterion (AIC) is used to performs stepwise model selection.
  • Model fits are ranked according to their AIC values, and the model with the lowest AIC value is sometime considered the 'best'.

Model selection suggested by AIC


                

Explanations
  • ROC curve: receiver operating characteristic curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied
  • ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings
  • Sensitivity (also called the true positive rate) measures the proportion of actual positives that are correctly identified as such
  • Specificity (also called the true negative rate) measures the proportion of actual negatives that are correctly identified as such

Prediction

Prepare model first


Step 4. Test Set Preparation


Data: Breast Cancer


Data for prediction should cover all the variables in the model

2. Show 1st row as column names?

3. Use 1st column as row names? (No duplicates)

Correct separator and quote ensure the successful data input

Find some example data here

If the model and new data are ready, click the blue button to generate prediction results.





Output 3. Prediction Results



Predicted dependent variable is shown in the 1st column


This plot is shown when new dependent variable is provided in the test data.

This plot shows the ROC plot between predicted values and true values, based on the new data not used in the model.

Sensitivity and specificity table