2. Discuss Linear Regression with an example.
Question
- Discuss Linear Regression with an example.
Solution
Linear Regression is a fundamental algorithm in machine learning that predicts a dependent variable value (y) based on a given independent variable (x). So, this regression technique finds out a linear relationship between x (input) and y(output). Hence, the name is Linear Regression.
Let's take an example to understand it better:
Suppose we want to predict the price of a house based on its area. We have a dataset of houses where we know the area of each house and the price it was sold for.
Step 1: Plot the data First, we plot the data on a graph with the area on the x-axis and the price on the y-axis. Each point on the graph corresponds to a house.
Step 2: Fit a line Next, we try to fit a line through the data. This line is our regression line, and we try to fit it in such a way that the total distance between the line and all the points is as small as possible.
Step 3: Predict the price Now, if we want to predict the price of a house given its area, we find the area on the x-axis, draw a line up to the regression line, and then draw a line from there to the y-axis. The point where it hits the y-axis is the predicted price of the house.
The equation of the regression line is of the form y = mx + c, where m is the slope of the line and c is the y-intercept. The slope m represents the rate of change of y as x changes. In our example, it represents how much the price changes for a unit change in the area. The y-intercept c represents the price of a house when the area is zero.
Linear Regression is a simple yet powerful algorithm that is widely used in machine learning and statistics. It is easy to understand and interpret, and it forms the basis for many other machine learning algorithms.
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