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The vertical distance between the observed responses in the dataset and the line of best fit is called the residual
error (e) as shown in the graph below:
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Marks (Y) 60 residual (e)=Observed value -- Predicted Value
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No. of Hours Studied (X)
Regression—How good is the Line?
1. Linear regression aims to find the best-fitting straight line through the points.
2. If data points are closer to the line of best fit (less residual error), it means the correlation between the two
variables is higher. That means, the relationship between the two variables is strong.
3. The regression line is also called ‘Line of Least Squares of Errors’ because the lower the residual errors, the
better.
4. Each data point has one residual.
#Digital Literacy
Video Session
Scan the QR code or visit the following link to watch the video: Linear Regression
Algorithm
https://www.youtube.com/watch?v=E5RjzSK0fvY&t=527s
Brainy Fact
The least squares regression method was first published by mathematicians Legendre in 1805
and Carl Friedrich Gauss in 1809. Both used linear regression to predict the movement of planets
around the sun. Gauss later published an improved method in 1821.
When Regression Analysis is Not Suitable
It’s important to understand that regression analysis may not always be suitable in certain scenarios:
● No Correlation: If there is no correlation between the variables, meaning they change independently of each
other, regression analysis will not yield meaningful insights or predictions.
330 Touchpad Artificial Intelligence (Ver. 3.0)-XI

