The data contains the following columns:

1. Price/Book Value Ratio - Corresponding to $Y$ (the dependent variable).
2. Return on Equity - Corresponding to $X_1$ (an independent variable).
3. Growth% - Corresponding to $X_2$ (another independent variable).

Now let's proceed with solving the tasks as per your request.

Part 1: Regression Model based on Return on Equity ( $X_1$ )

We'll develop the regression model: $\hat{Y} = 2.3197 + 0.0706X_1$

Part 2: Regression Model based on Growth ( $X_2$ )

We'll develop this model: $\hat{Y} = 3.1253 + 0.0310X_2$

Part 3: Regression Model based on both Return on Equity and Growth ( $X_1, X_2$ )

This model is: $\hat{Y} = 1.9298 + 0.0605X_1 + 0.0219X_2$

Part 4: Compute and interpret the adjusted $R^2$

We'll now calculate the adjusted $R^2$ values for all three models.The adjusted $R^2$ values for the three models are as follows:

1. Model 1 (based on Return on Equity $X_1$): Adjusted $R^2 = 33.5\%$
2. Model 2 (based on Growth $X_2$): Adjusted $R^2 = 19.2\%$
3. Model 3 (based on Return on Equity and Growth $X_1, X_2$): Adjusted $R^2 = 42.3\%$

Interpretation:

• Model 1 explains 33.5% of the variation in the Price-to-Book Value ratio, corrected for the number of predictors.
• Model 2 explains 19.2% of the variation, indicating Growth has a lower explanatory power than Return on Equity.
• Model 3 improves the explanatory power to 42.3%, showing that using both variables provides a better fit.

Do you want more details or have any questions?

Here are 5 questions related to the analysis:

1. What does the adjusted $R^2$ account for that regular $R^2$ does not?
2. How can the coefficients from the models be interpreted in practical terms?
3. What other factors might improve the prediction of Price-to-Book Value Ratio?
4. Why might Return on Equity be a stronger predictor than Growth in this case?
5. How can you test the significance of each predictor in these models?

Tip: Adjusted $R^2$ is useful when comparing models with different numbers of predictors, as it penalizes the addition of non-significant variables.