INTRODUCTION – Logistic Regression
In this segment, participants are going to learn binomial logistic regression-a statistical method that classifies data into two different classes. The first exploration seems to cover thoroughly the theory and techniques involved in binomial logistics regression. Students should possess an excellent understanding of theory and practice in developing and interpreting such regression models.
At each stage of learning, the participant will experience the usage of binomial logistic regression about practical applications in data analysis of all forms. There will focus and debate on how best this regression mode allows us to model data and how the participants will end up holding onto such skills to make decisions from their contexts. An experienced data professional will apply all the theoretical and practical approaches to make confident use of binomial logistic regression.
Learning Objectives:
- Distinguish binomial logistic regression from log-linear regression
- Conduct a log-linear Poisson regression
- Run a multinomial logistic regression in Python.
- Interpret the outcome from a binomial logistic regression model
- Evaluate the performance of a binomial logistic regression model
- Define confusion matrix, ROC, AUC, precision, recall, and type 1 and type 2 errors in the context of binomial logistic regression
- Run a binomial logistic regression in Python.
- Delineate the basic assumptions of binomial logistic regression.
- State the importance of the data properties taken into consideration when comparing two regression models.
- Understand the sigmoid function in a binomial logistic regression instance.
- Define binomial logistic regression and it in relation to use.
PRACTICE QUIZ: TEST YOUR KNOWLEDGE: FOUNDATIONS OF LOGISTIC REGRESSION
1. No extreme outliers is one of the four main binomial logistic regression assumptions. What are the other three? Select all that apply.
- Homoscedasticity
- Linearity (CORRECT)
- Independent observations (CORRECT)
- No multicollinearity (CORRECT)
Correct: The fundamental assumptions of binomial logistic regression processes involve linearity, independence of observations, lack of multicollinearity, and there should be no extreme outliers.
2. Logit is the logarithm of the odds of a given probability.
- True (CORRECT)
- False
Correct: The logit, which is the relationship between the odds and log of an event probability may be taken as using this for creating linear associations between probabilities of events and independent variables.
3. Fill in the blank: The maximum likelihood estimation is a technique used for estimating the beta parameters that _____ the likelihood of a model producing the observed data.
- control
- balance
- maximize (CORRECT)
- reduce
Correct: It is a methodology developed for estimating beta parameters, which would have maximized the likelihood of the model generating the given observed data.
PRACTICE QUIZ: TEST YOUR KNOWLEDGE: LOGISTIC REGRESSION WITH PYTHON
1. When building a logistic regression model, what does CLF stand for?
- Claimer
- Codifier
- Connector
- Classifier (CORRECT)
2. Which package do you use to create a plot of your model to visualize its results?
- Dashboard package
- Matrix package
- Results package
- Seaborn package (CORRECT)
PRACTICE QUIZ: TEST YOUR KNOWLEDGE: INTERPRET LOGISTIC REGRESSION RESULTS
1. The confusion matrix is a graphical representation of how accurate a classifier is at predicting what for a categorical variable?
- Validity
- Errors
- Labels (CORRECT)
- Precision
Correct: This is the confusion matrix, which indicates how accurate a classifier is at predicting the labels for a categorical variable. It indicates the number of data points correctly classified for each category, while the other cells indicate how many points are misclassified.
2. Fill in the blank: _____ measures the proportion of positive predictions that were true positives.
- Accuracy
- Validity
- Precision (CORRECT)
- Recall
Correct: Precision is the ratio of true positive to positive predictions.
3. Which of the following provide additional information about the likelihood of a result being merely by chance? Select all that apply.
- Maximum likelihood estimation
- Logit
- Confidence intervals (CORRECT)
- P-value (CORRECT)
Correct: Furthermore, the perception of the results being chance results can be substantiated by additional evidence. The p-value serves to measure the significance of results in statistical terms, while the confidence intervals return a set of values that would accommodate the true parameter within its bounds.
PRACTICE QUIZ: TEST YOUR KNOWLEDGE: COMPARE REGRESSION MODELS
1. Which model might a data professional consider first if the outcome variable is binary?
- Single linear regression
- Multiple linear regression
- Binomial logistic regression (CORRECT)
- Hypothesis testing
Correct: If the outcome variable is binary, a data professional may opt for a binomial logistic regression model. After constructing the model, the best way to determine whether logistic regression is appropriate is to evaluate its performance with various metrics.
2. A data professional can use recall to evaluate a logistic regression model. What other metrics can be used to meet this goal? Select all that apply.
- R squared
- Precision (CORRECT)
- Confusion matrices (CORRECT)
- P-value (CORRECT)
Correct: A data professional would use a variety of measurement techniques such as recall, precision, p-value, and confusion matrices to evaluate the performance of a logistic regression model. Such metrics evaluate the model in terms of accuracy, true positive identification, and significance associated with the results.
QUIZ: MODULE 5 CHALLENGE
1. Fill in the blank: Binomial logistic regression is a technique that models the _____ of an observation falling into one of two categories, based on one or more independent variables.
- Probability (CORRECT)
- determinant
- implications
- causations
2. A data professional calculates a logarithm of the odds of a given probability. What are they calculating?
- Likelihood
- Precision
- Logit (CORRECT)
- Recall
3. Fill in the blank: Maximum likelihood estimation is a technique for estimating the _____ that maximize the likelihood of the model producing the observed data.
- beta parameters (CORRECT)
- continuous coefficients
- error terms
- continuous parameters
4. Following the no extreme outlier assumption, when are outliers detected?
- Either before or after the model is fit
- After the model is fit (CORRECT)
- Before the model is fit
- While the model is being fit
5. What graphical representation demonstrates a classifier’s accuracy at predicting the labels for a categorical variable?
- Logistic matrix
- Logistic graph
- Likelihood matrix
- Confusion matrix (CORRECT)
6. A data professional calculates precision in logistic regression results. They have 101 true positives, 63 true negatives, 4 false positives, and 2 false negatives. What is the calculation for precision?
- 101 / (101 + 4) (CORRECT)
- (101 + 2) / 4
- (63 + 4) / 101
- 101 / (63 + 2)
7. A data professional calculates accuracy in logistic regression results. They have 99 true positives, 91 true negatives, and 248 total predictions. What is the calculation for accuracy?
- 248 / (99 + 91)
- (248 – 99) / 91
- 99 / (248 – 91)
- (99 + 91) / 248 (CORRECT)
8. A data professional calculates recall in logistic regression results. They have 145 true positives, 128 true negatives, 4 false positives, and 2 false negatives. What is the calculation for recall?
- 145 / (145 + 2) (CORRECT)
- (128 + 2) / 128
- (145 + 128) / (4 + 2)
- (4 – 2) / 145
9. What technique models the probability of an observation falling into one of two categories, based on one or more independent variables?
- Maximum likelihood estimation
- Linear regression
- Log-odds function
- Binomial logistic regression (CORRECT)
10. What is the logit formula?
- Logarithm of p divided by 1 minus p (CORRECT)
- Logarithm of 1 divided by p minus 1
- Logarithm of p plus 1 divided by p
- Logarithm of 1 plus p divided by p
11. What technique estimates the beta parameters that increase the likelihood of the model producing observed data?
- Precision
- Maximum likelihood estimation (CORRECT)
- Recall
- Accuracy
12. Which regression assumption states that, if multiple X variables are in a model, they should not be highly correlated with one another?
- Linearity
- No multicollinearity (CORRECT)
- Independent observations
- No extreme outliers
13. Fill in the blank: A confusion matrix is a graphical representation of how accurate a classifier is at _____ the labels for a categorical variable.
- spacing
- predicting (CORRECT)
- organizing
- limiting
14. A data professional calculates precision in logistic regression results. They have 89 true positives, 83 true negatives, 3 false positives, and 1 false negative. What is the calculation for precision?
- 89 / (83 + 1)
- (89 + 1) / 3
- (83 + 3) / 89
- 89 / (89 + 3) (CORRECT)
15. A data professional calculates accuracy in logistic regression results. They have 82 true positives, 75 true negatives, and 202 total predictions. What is the calculation for accuracy?
- (82 + 75) / 202 (CORRECT)
- 202 / (82 + 75)
- 82 / (202 – 75)
- (202 – 82) / 75
16. A data professional calculates recall in logistic regression results. They have 91 true positives, 84 true negatives, 6 false positives, and 5 false negatives. What is the calculation for recall?
- (84 + 5) / 84
- 91 / (91 + 5) (CORRECT)
- (91 – 6) / (84 – 5)
- 84 / (84 + 6)
17. Logit includes which other probability formula?
- Precision
- Odds (CORRECT)
- Recall
- Estimation
18. Fill in the blank: A confusion matrix is a graphical representation of how accurate a classifier is at predicting the labels for a _____ variable.
- Categorical (CORRECT)
- Confidence
- correlated
- continuous
19. Precision measures the proportion of positive predictions that were false positives.
- True
- False (CORRECT)
Correct: Precision is the fraction of positive predictions that actually are true positives. It is calculated as the number of true positives divided by the sum of true positives and false positives.
20. A data professional calculates accuracy in logistic regression results. They have 87 true positives, 94 true negatives, and 222 total predictions. What is the calculation for accuracy?
- 222 / (87 + 94)
- (87 + 94) / 222 (CORRECT)
- (222 – 87) / 94
- 87 / (222 – 94)
21. A data professional calculates recall in logistic regression results. They have 99 true positives, 80 true negatives, 7 false positives, and 4 false negatives. What is the calculation for recall?
- 80 / (80 + 7)
- (99 – 7) / (80 – 4)
- (84 + 4) / 80
- 99 / (99 + 4) (CORRECT)
22. Fill in the blank: Maximum likelihood estimation is a technique for _____ the beta parameters that maximize the likelihood of a model producing the observed data.
- Limiting
- duplicating
- eliminating
- estimating (CORRECT)
23. For the binomial logistic regression linearity assumption, there should be a linear relationship between each X variable and what logit probability?
- X equals 1
- Y equals 0 (CORRECT)
- X equals Y
- Y equals 1
CONCLUSION – Logistic Regression
To sum up, a detailed taking has been made by the participants on the various knots of binomial logistic regression, which is an important statistical method of data analysis. It has taught not just the theoretical background of binomial logistic regression, but also given practice to participants in creating and interpreting regression models.
Now participants are ready to use this knowledge while delving into real-life situations and making full use of binomial logistic regression as a tool for power data classification and revelation of deep insights. This basic understanding empowers data professionals to enrich their capabilities significantly in the area of decision-making across disciplines.