Let's break down the problem step by step. The image you've uploaded contains two parts of a regression analysis question involving multiple predictors. Here's a summary of each part of the question:

Part (a)

You are asked to show the following equation: $SSR(X_1, X_2, X_3) = SSR(X_1) + SSR(X_2 | X_1) + SSR(X_3 | X_1, X_2)$ Where:

• $SSR(X_1, X_2, X_3)$ is the sum of squares for the full model with all predictors $X_1, X_2, X_3$.
• $SSR(X_1)$ is the sum of squares for the model with just $X_1$.
• $SSR(X_2 | X_1)$ is the additional sum of squares added by including $X_2$ after $X_1$.
• $SSR(X_3 | X_1, X_2)$ is the additional sum of squares added by including $X_3$ after $X_1$ and $X_2$.

This equation is a property of sum of squares in regression analysis, where the total variance (SSR) in the full model can be decomposed into the individual contributions of each predictor.

Part (b)

This part deals with testing the significance of the regression model. Specifically, you need to:

• Test hypotheses on the coefficients $\beta_1 = -1.0$ and $\beta_2 = 0$.
• The error sum of squares (SSE) for the full model and the reduced model are provided.

The five subparts for part (b) ask you to:

1. State the null and alternative hypotheses.
2. State the full and reduced models.
3. Compute the test statistic (likely an F-statistic).
4. State the decision rule for hypothesis testing.
5. State the conclusion based on the hypothesis test.

Let me know if you'd like to proceed with solving any part of this problem, or if you'd like me to break down any of the steps further.

Would you like to proceed with the detailed solution?