Linear Regression vs Logistic Regression: A Detailed Comparison

When it comes to linear vs logistic regression, the differences are that linear regression handles regression problems while logistic regression is utilized for handling classification problems. The Regression Model helps e-commerce businesses in decision-making with various functions. Going for the best Machine Learning course will help you ace key concepts and fundamentals of deep learning and machine learning. Alongside this, you can understand the difference between linear regression and logistic regression and the importance of Regression with Linear and Logistic Regression in Machine Learning.

What is Linear Regression?

Linear Regression is one of the important Machine Learning algorithms to solve regression in real-time. The dependent variable for the Linear Regression model is continuous in nature. The variables X (independent variable) and Y (dependent variable) vary linearly with respect to time.

The linear relationship is highly dependent on both X and Y. For example, in E-commerce sales, stock (Y) price is dependent on time (X). For the independent value, the nature of the dependent value has changed. It is the probability of occurrence of an event that is continuous.

If the dependent variable varies with more than one independent variable, then it is known as the multiple Linear Regression method. The overall goal of using Linear Regression is to evaluate the best possible value of the given problem.

What Is Logistic Regression?

The term Logistic Regression is another important Machine Learning algorithm to solve classification problems in real-time. The dependent variable for the Logistic Regression model is binary in nature. The variables X (independent variable) and Y (dependent variable) vary linearly over time.

Logistic Regression is used in the forecasting company to find common problems in nature, like whether the rain will come or not. The output is classified as 0 or 1, not in between. The graph obtained is curvy or sigmoidal between 0 and 1.

Linear Regression vs Logistic Regression Head-to-Head Comparison

Let’s quickly understand the difference between linear and Logistic Regression.

Difference Between Linear Regression and Logistic Regression in Detail

Linear Regression is primarily known to determine the regression problems using Machine Learning algorithms from supervised learning. While Logistic Regression determines the classification problems which are categorical in nature.

First, we understand what supervised learning is and then discuss a bit about the classification problems before proceeding to the detailed comparison between Linear Regression and Logistic Regression.

Supervised Learning is performed on the labeled datasets, which means the datasets are already trained. It is of two types; classification and regression. The classification method helps to predict the object’s category based on different functions. Regression is used to determine continuous output with the independent variables.

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1. Linear Regression vs Logistic Regression: Steps Involved

Let’s understand what steps are required to evaluate linear vs Logistic Regression of a problem. The main goal is to achieve minimum loss such that the result comes under the best-fitted line.

Steps Involved in Linear Regression:

Step 1:The function Y is dependent in nature on the X variable. The equation form for the best-fitted line is Y= b0 + b1x + c, where x is the independent variable, y is the response variable, c is the error term, b0 is constant, and b1 is a slope.

Step 2:Use the hit-and-trial method to assign random variables to calculate the coefficients of the equation. Y is the output of the equation.

Step 3:As the output value (y^) is obtained, we can predict whether it is correct or not. If any error occurs, then we can calculate it using the mean squared error method and call it a loss function.

Loss function, L= 1/n summation ((y-y^) power 2), n is no. of observations

Step 4:Once the loss function is calculated, then we should minimize it with the gradient descent method.

Steps Involved in Logistic Regression:

Similarly, we determine the Logistic Regression of the function. Let’s proceed,

Step 1:The Logistic Regression is used to predict the binary values of the Linear Regression steps. For this, first, we decide the threshold, and if the resultant value is higher, then we classify it among the group.

The Logistic Regression equation is calculated as

log [y/1-y] = b0 + b1x + b2x1 +.... + bnxn.

Step 2:In Logistic Regression, the resultant value is very close to the actual value without any error or outlier. If the output is prone to errors, then we feed the values in a sigmoidal curve rather than a linear slope.

The sigmoidal curve represents by s (x)= 1/1+e^(-x)which obtains values between 0 and 1.

Step 3:Let's say we fix the threshold value to 0.5, then we obtain value respect to it as 0 and 1 using the sigmoidal function. And set the values to binary classification.

2. Linear Regression vs Logistic Regression: Formula

• Linear Regression formula:

y=b0+b1x+c,

where y is a dependent variable, b0 is the y-intercept, b1 is a slope, x is an independent variable, c is error

Gradient descent:

It is nothing but to minimize the cost function. The cost function finds out an error in the function, and if it exists, then minimizes it. The loss function is the difference between the predicted value and the actual value.

Take the first-order derivative of the function. The model keeps on repetition till it finds the best value. The main goal of Machine Learning is to find the minimum value of cost function or global minima. To achieve this, we set a threshold value to meet zero value.

• Logistic Regression formula:

log(Y/(1-Y)) = C+B1X1+B2X2+......

where y is the probability of an event happening

X1 and X2 are the two independent variables

C is the constant term

3. Linear Regression vs Logistic Regression: Cost Function

The cost function calculates the error of the function, which is the difference between the actual value and the predicted value. The resultant graph obtained by the loss

function is parabolic in nature due to a mean square error occurring in the predicted value. Our goal is to minimize the loss function as the cost values reach the bottom of the curve.

The loss function is solved using a first-order derivative. The process repeats till we reach global minima and then set the threshold value. Once we obtain the loss function, the final equation has evolved. Then we find the value of the Y variable for the X variable. For example, If the event occurring belongs to 0.6 value, then it neither belongs to class 1 nor class 0. Instead, the occurrence of an event is between both classes.

• Linear Regression Cost Function:

The cost function for linear regression is a mean squared error (MSE). MSE is calculated by taking the average square difference between the actual value and predicted values.

MSE = 1/N summation of (y - (mx+b)) ^2

• Logistic Regression Cost Function:

In Logistic Regression we can’t use MSE to obtain results, due to its non-linearity. Here we used Cross Entropy or Log Loss.

4. Linear Regression vs Logistic Regression: Dependent Variable

In multiple Linear Regression, there is a relationship between two or more independent variables and one dependent variable. At the same time, there is no such dependency in Logistic Regression. In linear regression, the output is continuous in nature, while logistic regression is binary in nature. Linear regression involves a solution that comes under a best-fitted curve. However, there is no such possibility with logistic regression.

5. Linear Regression vs Logistic Regression: Confusion Matrix

In linear vs Logistic Regression, the confusion matrix measure performance of classification models on a given set of data and evaluates any error made by classifiers. The output result will be of more than two categories. It is also known as an error matrix.

6. Linear Regression vs Logistic Regression: Overfit and Underfit

In the regression analysis, when the regression model includes every possible value of data points in the dataset. Then overfitting situation may occur.

7. Linear Regression vs Logistic Regression: Dependency Variable

In the Linear Regression, the relationship is linear between dependent and independent variables. While in the case of Logistic Regression, the relationship is non-linear or variable.

The Similarities Between Linear Regression and Logistic Regression

1. Linear and Logistic Regression in Machine Learning is performed using supervised algorithms. Supervised learning uses known sets of data to obtain a model which is used to predict response for the input values. It means that these algorithms use trained values of datasets. You can use supervised learning if you have existing data.
2. Both Linear Regression and Logistic Regression models work on linear equations that can be simply solved until the solution is best fitted and the loss function is minimized.
3. The Linear Regression and Logistic Regression used parametric regression. By parametric equations, we mean to say that they use linear equations for predictions.

These all are the similarities between Linear and Logistic Regression. Both algorithms have different ways of working, which we have already discussed above.

Linear vs Logistic Regression Use Cases

Linear Regression problem is used to evaluate the quantitative values of the problem. While Logistic Regression is used to evaluate the binary values or probabilities.

Talking about the Linear Regression vs Logistic Regression example to understand more: Both algorithms are using supervised learning but have different use cases.

1. Linear Regression Use Case: Linear Regression is used to predict business dependencies. Like the total number of road accidents caused due to reckless driving? Or what is the impact of drug dosage on blood pressure patients? LR is used to find stock prices and risks associated with it, find the game players' numbers for upcoming games, predict sales, student performance in the education sector, etc.
2. Logistic Regression Use Case: Logistic Regression is used to predict the probability of a result that would be continuous. For ex., determine the heart attack probability, number of students enroll in university, spam emails, etc.

Closing Comments

The respective blog is dedicated to understanding types of Regression and their comparison; Linear Regression vs Logistic Regression. These two algorithms are part of Machine Learning. The regression problems are commonly defined under Supervised Learning; the former is used to solve regression problems while the latter is used to help in classification problems in depth. Linear vs Logistic Regression is great for examining the prediction of the happening of a particular event. upGrad's best Machine Learning course will help you master supervised and unsupervised learning, regression and classifications.

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