The following data are obtained during an experiment involving 2 independent variables, y being the measured response.

It is assumed that the intercept 𝛽0 = 0 and the relationship is linear with 2 parameters

y = 𝛽1x1 + 𝛽2x2.

1. What is the associated least squares optimization problem?

2. Determine the model parameters.

3. What is the predicted value for x₁ = 3, x₂ = 1?

4. How would the problem be modified to include an interaction between the 2 predictors?