Logistic regression is a popular supervised learning algorithm used to predict categorical outcomes, converting linear regression outputs into probabilistic values via the sigmoid function. It comes in three types: binomial, multinomial, and ordinal, and has specific assumptions such as linearity and no multicollinearity. Applications span various fields including marketing, healthcare, finance, and social sciences, but limitations include interpretability issues and sensitivity to data quality.

1. Introduction to
Logistic
Regression
 Logistic regression is one of the most popular Machine Learning algorithms,
which comes under the Supervised Learning technique.
 Logistic regression predicts the output of a categorical dependent variable.
Therefore the outcome must be a categorical or discrete value. It can be
either Yes or No, 0 or 1, true or False, etc. but instead of giving the exact
value as 0 and 1, it gives the probabilistic values which lie between 0 and 1.
 Logistic regression is used for solving the classification problems.
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2. Types Of Logistic Regression:
Binomial: In binomial Logistic regression, there can be only two possible types of the dependent variables, such as 0 or 1, Pass
or Fail, etc.
Multinomial: In multinomial Logistic regression, there can be 3 or more possible unordered types of the dependent variable,
such as “cat”, “dogs”, or “sheep”
Ordinal: In ordinal Logistic regression, there can be 3 or more possible ordered types of dependent variables, such as “low”,
“Medium”, or “High”.

3. Sigmoid Function :
 The logistic regression model transforms the linear regression function continuous value output into categorical value
output using a sigmoid function.
 It maps any real value into another value within a range of 0 and 1.
 The value of the logistic regression must be between 0 and 1, which cannot go beyond this limit, so it forms a curve like the
"S" form. The S-form curve is called the Sigmoid function or the logistic function.
 𝛽0 is the y-intercept
 𝛽1 is the slope of the line
 x is the value of the x coordinate
 y is the value of the prediction
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4. Assumptions of Logistic Regression
1. Linearity: The relationship between the independent variables and the logit of the
dependent variable is linear.
2. No Multicollinearity: The independent variables should not be highly correlated with each other.
3. No Autocorrelation: The errors in the regression should be independent of each other.
4. Homoscedasticity: The variance of the errors should be constant across all levels of
the independent variables.
5. No Outliers: The model should not be unduly influenced by outliers in the data.
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6. Evaluating Logistic Regression Models
1
Model Accuracy
Measure the model's ability to
correctly classify instances into
the two classes using metrics like
accuracy, precision, recall, and F1-
score.
2 ROC Curve
Plot the true positive rate against
the false positive rate to visualize
the tradeoff between sensitivity
and specificity at different
probability thresholds.
3
Goodness of Fit
Assess how well the model fits
the data using tests like the
Hosmer-Lemeshow test or the
deviance statistic.
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7. Applications of Logistic Regression
Marketing and Sales
Predict customer purchasing behavior,
target marketing campaigns, and
identify high-value leads.
Healthcare
Diagnose medical conditions, assess
risk factors, and forecast patient
outcomes.
Finance
Assess credit risk, identify fraud, and
make investment decisions.
Social Sciences
Analyze survey data, predict voter
turnout, and study social phenomena.
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8. Limitations and Considerations
Interpretability
Logistic regression models can be less
interpretable than simpler models,
especially as the number of predictors
increases.
Linearity Assumption
The assumption of linearity between
the predictors and the log-odds may
not always hold, leading to biased
estimates.
Sensitivity to Data Quality
Logistic regression is sensitive to
missing data, outliers, and other data
quality issues, which can significantly
impact model performance.
Class Imbalance
When the classes are highly
imbalanced, logistic regression may
struggle to accurately predict the
minority class.
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