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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
  
2.3328plus
  
0.0700Upper 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
  
enter your response hereplus
  
enter your response hereUpper X Subscript 2 i
​(Round to four decimal places as​ needed.)

The dataset contains the following columns:

1. **Price/Book Value Ratio (Y)**: Dependent variable.
2. **Return on Equity (X₁)**: Independent variable for part a.
3. **Growth% (X₂)**: Independent variable for part b.

Let's start by developing the required regression models.

### Part a
The first model predicts the price-to-book value ratio (Y) based on return on equity (X₁). I'll calculate the coefficients now.

### Part b
The second model predicts the price-to-book value ratio (Y) based on growth percentage (X₂). I will compute that after completing the first part.For **Part a**, the regression model to predict the price-to-book value ratio (Y) based on return on equity (X₁) is:

\[
\hat{Y}_i = 2.3328 + 0.0700 \cdot X_{1i}
\]

Now, let's proceed with **Part b**, where we predict the price-to-book value ratio (Y) based on growth percentage (X₂). I'll calculate the coefficients for this next.For **Part b**, the regression model to predict the price-to-book value ratio (Y) based on growth percentage (X₂) is:

\[
\hat{Y}_i = 3.1233 + 0.0310 \cdot X_{2i}
\]

Do you need further details or clarifications on this? 

Here are five related questions to explore:

1. How do you interpret the coefficients in these regression models?
2. What are the assumptions of linear regression that should be checked?
3. How can we assess the goodness of fit for these models?
4. Would you like to analyze residuals for these models to check for any patterns?
5. How could we build a multiple regression model using both predictors (X₁ and X₂)?

**Tip**: When interpreting the slope in a regression, it represents the change in the dependent variable for a one-unit change in the independent variable.

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 based on the given data.

Learn how to develop linear regression models to predict price-to-book value ratio based on return on equity and growth percentage. Using a dataset of 71 drug companies, this tutorial covers core concepts of business valuation and regression analysis.

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