deriviation_of_a_and_b_in_a_simple_regression
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| deriviation_of_a_and_b_in_a_simple_regression [2025/08/04 21:22] – hkimscil | deriviation_of_a_and_b_in_a_simple_regression [2026/05/05 23:14] (current) – hkimscil | ||
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| dv for b | dv for b | ||
| to understand [[:gradient descent]] | to understand [[:gradient descent]] | ||
| + | see also [[:chain rules]] | ||
| [{{: | [{{: | ||
| Line 44: | Line 45: | ||
| \text{for b, (coefficient)} \\ | \text{for b, (coefficient)} \\ | ||
| \\ | \\ | ||
| - | \dfrac{\text{d}}{\text{dx}} \sum{(Y_i - (a + bX_i))^2} | + | \dfrac{\text{d}}{\text{db}} \sum{(Y_i - (a + bX_i))^2} |
| & = & \sum{2 (Y_i - (a + bX_i))} * (-X_i) \;\;\;\; \\ | & = & \sum{2 (Y_i - (a + bX_i))} * (-X_i) \;\;\;\; \\ | ||
| & \because & \dfrac{\text{d}}{\text{dv for b}} (Y_i - (a+bX_i)) = -X_i \\ | & \because & \dfrac{\text{d}}{\text{dv for b}} (Y_i - (a+bX_i)) = -X_i \\ | ||
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