In software development, predicting defects is essential for improving quality and reducing maintenance costs. This presentation demonstrates how to use logistic regression to estimate the probability of a module being defective based on metrics like Lines of Code (LOC) and Complexity.

Logistic regression models the probability of a binary outcome. The model is defined as:

\[ P(Y=1 \mid X) = \frac{e^{\beta_0 + \beta_1 X}}{1 + e^{\beta_0 + \beta_1 X}} \]

Here, Y = 1 indicates that a software module is defective, and X represents a software metric (for example, LOC).

To linearize the relationship, I used the logit transformation:

\[ \text{logit}(P) = \log\left(\frac{P}{1-P}\right) = \beta_0 + \beta_1 X \]

The odds ratio, which quantifies the change in odds for a one-unit increase in X, is given by:

\[ \text{Odds Ratio} = e^{\beta_1} \]

Below is the R code to simulate data for 100 software modules with two predictors: Lines of Code (LOC) and Complexity. The defect status is generated using a logistic model.

##        LOC Complexity defect
## 1 443.9524   7.868780      0
## 2 476.9823  10.770651      1
## 3 655.8708   9.259924      1
## 4 507.0508   8.957372      1
## 5 512.9288   7.145144      1
## 6 671.5065   9.864917      1

The following code creates a scatter plot of LOC vs. defect status using ggplot2. It uses jitter to better display the binary outcome and color-codes points by Complexity.

I fit a logistic regression model using both LOC and Complexity. For visualization, I fixed Complexity at its mean and plot the predicted probability of defect versus LOC.

The following code creates an interactive 3D plot showing the relationship among LOC, Complexity, and the predicted defect probability.

Logistic regression is an effective tool for predicting software defects using key metrics such as LOC and Complexity. This presentation demonstrates data simulation, model fitting, and visualization using ggplot2 and plotly.