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A financial analyst engaged in business valuation obtained financial data on 71 drug companies. Let Y correspond to the​ price-to-book value​ ratio, Upper X 1 correspond to the return on​ equity, and Upper X 2 correspond to the growth percentage. Use the accompanying data to complete parts a. through e. below.
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Part 1
a. Develop a regression model to predict​ price-to-book-value ratio based on return on equity.
ModifyingAbove Upper Y with caret Subscript iequals

2.3197plus

0.0706Upper X Subscript 1 i
​(Round to four decimal places as​ needed.)
Part 2
b. Develop a regression model to predict​ price-to-book-value ratio based on growth.
ModifyingAbove Upper Y with caret Subscript iequals

3.1253plus

0.0310Upper X Subscript 2 i
​(Round to four decimal places as​ needed.)
Part 3
c. Develop a regression model to predict​ price-to-book-value ratio based on return on equity and growth.
ModifyingAbove Upper Y with caret Subscript iequals

1.9298plus

0.0605Upper X Subscript 1 iplus

0.0219Upper X Subscript 2 i
​(Round to four decimal places as​ needed.)
Part 4
d. Compute and interpret the adjusted r squared for each of the three models.
Start with the part​ (a) model.
The adjusted r squared shows that

enter your response here​% of the variation in
▼
return on equity
price-to-book-value
is explained by
▼
return on equity
price-to-book-value

▼
after
before
correcting for the number of independent variables in the model.
​(Round to one decimal place as​ needed.)

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.

A financial analyst engaged in business valuation obtained financial data on 71 drug companies. Let Y correspond to the price-to-book value ratio, X1 correspond to the return on equity, and X2 correspond to the growth percentage. Develop regression models and compute the adjusted R squared for each model.

This problem demonstrates how to develop regression models to predict the price-to-book value ratio of 71 drug companies based on return on equity and growth percentage. It covers key statistical concepts like adjusted R-squared, linear regression models, and predictor interpretation.

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