the following data are obtained during an experiment involving 2 indep

Question

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?