Final answer:
To calculate the error deltas in multivariate linear regression, one must take the derivative of the cost function with respect to each weight coefficient. By doing this for the intercept and other coefficients, you determine by how much the error would change if the weight is altered.
Step-by-step explanation:
To compute the error deltas (D, w[0]), (D, w[1]), and (D, w[2]) in a multivariate linear regression, you first need to understand what each term represents. In the context of linear regression, w[0], w[1], and w[2] are the coefficients of the model, and D represents the data points. The error delta for each weight w[i] quantifies how much the error would change if the weight w[i] is changed by a small amount. This concept is used when performing gradient descent to update the weights in order to minimize the error function. Typically, in a squared error cost function, the error delta is computed as the derivative of the cost function with respect to the weight w[i].
Here's an example: Let's say you have a dataset D that consists of n data points and your multivariate linear regression model makes predictions using the equation y = w[0] + w[1]x1 + w[2]x2. To compute the error delta for weight w[1], you would take the partial derivative of the cost function with respect to w[1]. If the cost function is the mean squared error, the derivative would involve the sum of the product of the errors in predictions and the corresponding x1 values, divided by n. This process would be analogous for w[0] and w[2], using the respective features values and including the intercept term w[0] when necessary.