If the input to our linear regression object is of 10 dimensions, including the bias, how many variables does our cost or total loss function contain?1 point

To determine the number of variables in the cost or total loss function for a linear regression model with an input of 10 dimensions, including the bias, we can follow these steps:

1. ### Break Down the Problem

• We need to consider what each dimension represents in a linear regression model.
• Typically, in a linear regression model, each input feature contributes a coefficient (weight) to the model.

2. ### Relevant Concepts

• In linear regression, the model can be represented as: $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots + \beta_n x_n$ where $\beta_0$ is the bias term and $\beta_1, \beta_2, \ldots, \beta_n$ are the coefficients for each feature.

3. ### Analysis and Detail

• Given that we have 10 dimensions, this implies:
  • 1 dimension is for the bias term ($\beta_0$).
  • The remaining 9 dimensions correspond to features ($x_1, x_2, \ldots, x_9$).

4. ### Verify and Summarize

• Therefore, there will be a total of 10 variables in our loss function: 1 for the bias and 9 for the corresponding features.

Final Answer

The cost or total loss function contains 10 variables.