In linear regression, the terms "weight" and "bias" refer to the model parameters that define the relationship between the input features and the output prediction.
1. Weight:
In linear regression, the weight (also known as the coefficient) represents the slope of the linear relationship between the input features and the output prediction. For a simple linear regression with only one input feature, the model equation can be represented as:
y_pred = weight * x + bias
Here, `y_pred` is the predicted output, `x` is the input feature, `weight` is the parameter that determines how the input feature influences the prediction, and `bias` is the intercept of the linear equation.
2. Bias:
The bias (also known as the intercept) represents the value of the predicted output when the input feature is zero. It accounts for any constant offset or error in the prediction that is independent of the input features. In the model equation above, the bias `bias` is added to the product of `weight` and `x` to form the final prediction.
When training a linear regression model, the goal is to find the optimal values for `weight` and `bias` such that the model's predictions fit the training data as closely as possible. The process of finding these optimal values involves minimizing the Mean Squared Error (MSE) or another suitable loss function, as discussed in the previous answer.
In summary, weight determines the influence of the input feature on the prediction, and bias adjusts the prediction independently of the input features. Together, they form the equation of a straight line (in the case of simple linear regression) that best fits the data points in the training set.
