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Simple Linear Regression Algorithm In Machine Learning
What Is The Linear Regression Algorithm?
- Taller people tend to weigh more.
- Shorter people tend to weigh less.
Formula For Calculating A Straight Line
| Formula Part | Description |
|---|
| y | Average of target (or output variable) |
| x | Average of the Input variable |
| m | The slope (how much y changes for each x). The slope is also known as the Coefficient. |
| c | The intercept (where the line crosses the y-axis), i.e., what is the value of Y when X is zero? |
Example
| Height | Weight |
|---|
| 150 cm | 50 kg |
| 160 cm | 56 kg |
| 170 cm | 63 kg |
#average of x values (heights)
avg_x = (150 + 160 + 170) / 3 = 160
#average of y values (weights)
avg_y = (50 + 56 + 63) / 3 = 56.33
| x | y | xi - avg_x | yi - avg_y | (xi - avg_x)(yi - avg_y) | (xi - avg_x)² |
|---|
| 150 | 50 | -10 | -6.33 | 63.3 | 100 |
| 160 | 56 | 0 | -0.33 | 0 | 0 |
| 170 | 63 | 10 | 6.67 | 66.7 | 100 |
#Calculating the numerator for the calculation of slope
Σ[(x - avg_x)(y - avg_y)] = 63.3 + 0 + 66.7 = 130
#Calculating the denominator for the calculation of slope
Σ[(x - avg_x)²] = 100 + 0 + 100 = 200
#value of slope
m = 130/200 = 0.65
Error
Error = Y (Actual) – Y (Predicted)
y = (0.65)X +(-47.67) // mx + c
| Height | Weight (Actual) | Weight (Predicted) – Calculation | Weight (Predicted) | Error |
|---|
| 150 | 50 | 0.65×150−47.67 | 49.83 | 0.17 |
| 160 | 56 | 0.65×160−47.67 | 56.33 | -0.33 |
| 170 | 63 | 0.65×170−47.67 | 62.83 | 0.17 |
Root Mean Squared Error (RMSE)
| Posted By - | Karan Gupta |
| |
| Posted On - | Tuesday, May 20, 2025 |
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| Updated On - | Saturday, September 27, 2025 |