Linear regression equation: ŷ = β0 + β1X
Regression analysis
Linear regression equation: ŷ = β0 + β1X
Linear regression aims to predict the dependent variable (ŷ) using the independent variable (X) and its relationship with the dependent variable. The equation includes a y-intercept (β0) and a slope (β1), which represent the starting point and the rate of change, respectively.
Example
If we want to predict a person's weight (ŷ) based on their height (X), the linear regression equation could be ŷ = 50 + 2X, where 50 is the y-intercept and 2 is the slope.
Understanding the linear regression equation is crucial for making accurate predictions and interpreting the relationship between variables in statistical modeling.
Related concepts
Gradient descent
Gradient descent weight update equation: w := w - α * ∇J(w)
Adam optimizer weight update with m and v terms
Adam optimizer weight update: w_t = w_{t-1} - α * m_t / (sqrt(v_t) + ε)
Matrix norm
L1 norm of a vector is the sum of absolute values of its components
Normalization (machine learning)
L2 normalization equation: x_i' = x_i / ||x||_2
Mean squared error
Mean squared error (MSE) formula: MSE = (1/n) * Σ(y_i - ŷ_i)²
ReLU and Leaky ReLU
ReLU: f(x) = max(0, x); Leaky ReLU: f(x) = x if x > 0 else αx (α < 1)
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