1. The problem is to find the values of \(\beta_0, \beta_1, \beta_2\) that minimize the sum of squared differences given by $$\sum_{i=1}^{30} \left( \text{Milk Yield}_i - \beta_0 - \beta_1 \times \text{Body Weight}_i - \beta_2 \times \text{Age}_i \right)^2$$ 2. This is a standard multiple linear regression problem where Milk Yield is the dependent variable and Body Weight and Age are independent variables. 3. To minimize the sum, we take partial derivatives of the sum with respect to \(\beta_0, \beta_1, \beta_2\) and set them equal to zero: $$\frac{\partial}{\partial \beta_j} \sum_{i=1}^{30} \left( y_i - \beta_0 - \beta_1 x_{1,i} - \beta_2 x_{2,i} \right)^2 = 0 \quad \text{for } j = 0,1,2,$$ where \(y_i = \text{Milk Yield}_i\), \(x_{1,i} = \text{Body Weight}_i\), and \(x_{2,i} = \text{Age}_i\). 4. This gives the normal equations: $$\sum_{i=1}^{30} (y_i - \beta_0 - \beta_1 x_{1,i} - \beta_2 x_{2,i}) = 0$$ $$\sum_{i=1}^{30} (y_i - \beta_0 - \beta_1 x_{1,i} - \beta_2 x_{2,i}) x_{1,i} = 0$$ $$\sum_{i=1}^{30} (y_i - \beta_0 - \beta_1 x_{1,i} - \beta_2 x_{2,i}) x_{2,i} = 0$$ 5. Solving these simultaneous equations yields the values of \(\beta_0, \beta_1, \beta_2\) that minimize the sum of squared residuals. 6. In matrix form, if \(X\) is the 30x3 matrix with a column of ones for \(\beta_0\), \(x_{1,i}\), and \(x_{2,i}\), and \(Y\) is the 30x1 vector of milk yields, then: $$ \hat{\beta} = (X^T X)^{-1} X^T Y $$ This vector \(\hat{\beta}\) contains the minimizing parameters. 7. This is a standard least squares multiple regression solution used in statistical modeling contexts.