Understanding Simple Linear Regression


Introduction: In the world of machine learning, predicting outcomes based on available data is a common challenge. Consider the scenario where a friend seeks your assistance in predicting the price of a new house in a particular locality. Without any information about the features of the houses, this task seems insurmountable. However, through the power of mathematics and regression, we can unravel the mystery behind house prices. In this blog, we will delve into the concept of Simple Linear Regression using an illustrative example to comprehend how this technique can help us predict the price of the next house.

The Example: Imagine four colonies, each with its corresponding house price: h1 - 40 lakhs, h2 - 70 lakhs, h3 - 75 lakhs, and h4 - 30 lakhs. Our goal is to predict the price of the next house in h5. Initially, we lack any feature information for the houses, making prediction challenging. But fret not; regression comes to our rescue.

Plotting the Graph: To understand the data better, we plot the house prices against their respective colonies. The dotted lines on the graph represent average values. While these averages might not be exact, they give us a rough idea of where the predicted price lies. Now, we must calculate the error or loss for each house to assess the accuracy of our predictions.


Calculating the Loss (Sum of Squared Errors): By subtracting the predicted value from the actual value for each house, we obtain the error values: h1 = -5, h2 = +3, h3 = +7, and h4 = -9. To quantify the total error, we square these values and add them up. The sum of squared errors (SSE) is then computed as 164. Squaring the errors is essential to prevent ideal situation error values from canceling each other out.

Incorporating House Features: Now, imagine your friend provides you with another crucial piece of information: the area of the respective houses - 60, 75, 90, and 40 square meters, respectively. With this additional feature, we can create a new graph by plotting the house areas against their prices.

The Concept of Independent and Dependent Variables: In this context, area becomes the independent variable, while the house price remains the dependent variable. We represent the independent variable on the x-axis and the dependent variable on the y-axis. Plotting the data points and joining them with a line, we create a regression line. It could be either straight or curved, depending on the data distribution.



Minimizing SSE and Predicting h5 Price: The objective now is to minimize the SSE by adjusting the regression line. By doing so, we achieve a line that best fits the data points, enabling more accurate predictions. The SSE value reduces to 11, demonstrating the improved performance of our regression model. With the feature information and the area of h5 (70 square meters), we can effortlessly predict the house price. Drawing a vertical line from the area value on the x-axis until it intersects the regression line, we find that the predicted price lies between 40 and 70 lakhs. Therefore, the estimated price of h5 is 60 lakhs.

Conclusion: Simple Linear Regression serves as a powerful tool to predict outcomes when equipped with the appropriate features. In our example, we witnessed how incorporating the house area as an independent variable drastically improved the accuracy of our predictions. Whether it's house prices, stock market trends, or medical data, regression techniques provide valuable insights into the relationships between variables, making it an indispensable asset in the realm of machine learning.

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