To answer the parts of the question systematically, let’s start with Part a: identifying the sample estimates of $\beta_0$, $\beta_1$, and $\beta_2$. These estimates are taken directly from the software output.

a. Sample Estimates of $\beta_0$, $\beta_1$, and $\beta_2$:

From the regression equation and the table of coefficients:

1. $\hat{\beta}_0 = 1864.4$ (Constant)
2. $\hat{\beta}_1 = -759.33$ (Coefficient of $X_1$)
3. $\hat{\beta}_2 = -355.07$ (Coefficient of $X_2$)

Thus: $\hat{\beta}_0 = 1864.4, \quad \hat{\beta}_1 = -759.33, \quad \hat{\beta}_2 = -355.07$

Next Steps:

Would you like me to move forward with additional parts, such as evaluating significance, interpreting the results, or analyzing $R^2$ and ANOVA values? Let me know!

Five Follow-Up Questions:

1. How do you interpret the coefficients ($\beta_1$ and $\beta_2$) in the context of the regression model?
2. What does the p-value of each predictor tell us about its significance in the model?
3. How do the $R^2$ and adjusted $R^2$ values influence your interpretation of the model's fit?
4. What is the meaning of the residual standard error ($S$) in the context of this model?
5. Can you assess the overall model significance from the ANOVA $F$-statistic and p-value?

Tip:

Always consider both the magnitude and the p-value of regression coefficients when evaluating their impact on the dependent variable. This ensures you consider practical significance alongside statistical significance.