1. **Problem:** Fit a multiple regression model predicting milk yield using cow body weight and age as predictors. 2. **Step 1: Define the regression model.** The multiple linear regression model can be expressed as: $$\text{Milk Yield} = \beta_0 + \beta_1 \times \text{Body Weight} + \beta_2 \times \text{Age} + \epsilon$$ where: - $\beta_0$ is the intercept, - $\beta_1$ is the coefficient for body weight, - $\beta_2$ is the coefficient for age, - $\epsilon$ is the error term. 3. **Step 2: Fit the model using data.** Using the data for 30 cows, estimate $\beta_0$, $\beta_1$, and $\beta_2$ by methods such as least squares. This involves minimizing the sum of squared residuals: $$\min_{\beta_0, \beta_1, \beta_2} \sum_{i=1}^{30} \big( \text{Milk Yield}_i - \beta_0 - \beta_1 \times \text{Body Weight}_i - \beta_2 \times \text{Age}_i \big)^2$$ 4. **Step 3: Interpret the regression coefficients.** - $\beta_0$: The expected milk yield when body weight and age are zero (baseline level). - $\beta_1$: The change in milk yield for each unit increase in body weight, holding age constant. - $\beta_2$: The change in milk yield for each unit increase in age, holding body weight constant. 5. **Step 4: Discuss management implications.** - If $\beta_1$ is positive and significant, increasing cow body weight could lead to higher milk yields, suggesting nutrition or health management focus. - If $\beta_2$ is negative or positive, age impacts milk production; decisions on breeding or replacement strategies can be informed. - Overall, model helps target interventions to improve milk yield by managing weight and age factors.