Predicter Models (10 marks):a) Name and explain 2 major differences between linear regression and logistic regression.b) Name and explain 3 features linear regression and logistic regression have in common.
Question
Predicter Models (10 marks):a) Name and explain 2 major differences between linear regression and logistic regression.b) Name and explain 3 features linear regression and logistic regression have in common.
Solution
a) Differences between Linear Regression and Logistic Regression:
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Outcome Variable: The first major difference between linear regression and logistic regression lies in what they're trying to predict. Linear regression is used to predict a continuous outcome variable (dependent variable). For example, predicting house prices, stock prices, etc. On the other hand, logistic regression is used to predict a categorical or discrete outcome variable, often binary in nature. For example, predicting whether an email is spam or not, or if a tumor is malignant or benign.
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Equation: The second major difference is the equation used in the prediction. Linear regression uses a linear function to predict the outcome variable. The equation is Y = a + bX + e, where Y is the dependent variable, X is the independent variable, a is the Y-intercept, b is the slope, and e is the error term. On the other hand, logistic regression uses a logistic function to predict the probability of the outcome variable. The equation is p(X) = e^(a + bX) / (1 + e^(a + bX)), where p(X) is the probability of the positive class.
b) Common Features of Linear Regression and Logistic Regression:
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Supervised Learning Models: Both linear regression and logistic regression are supervised learning models. This means that they both require labeled training data to learn the relationship between the input (independent variables) and output (dependent variable).
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Coefficient Estimation: Both models use the method of Maximum Likelihood Estimation (MLE) to estimate the coefficients of the independent variables. MLE is a method of estimating the parameters of a statistical model, given observations.
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Assumption of Linearity: Both linear regression and logistic regression assume a linear relationship between the independent variables and the log odds of the dependent variable. However, logistic regression transforms this relationship with the logistic function to predict probabilities.
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