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A financial analyst engaged in business valuation obtained financial data on 

7171 

drug companies. Let Y correspond to the​ price-to-book value​ ratio, 

Upper X 1X1 

correspond to the return on​ equity, and 

Upper X 2X2 

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 iYiequals=enter your response hereplus+enter your response hereUpper X Subscript 1 iX1i

​(Round to four decimal places as​ needed.)

The data includes three columns:

1. **Price-to-Book Value Ratio** (dependent variable, \( Y \))
2. **Return on Equity** (independent variable \( X_1 \))
3. **Growth Percentage** (independent variable \( X_2 \), not used in this part of the question)

Now, let's develop a simple linear regression model where the **Price-to-Book Value Ratio** is predicted based on **Return on Equity** (\( X_1 \)).

The regression model will be in the form:
\[
\hat{Y}_i = \beta_0 + \beta_1 X_{1i}
\]
We'll compute the coefficients \( \beta_0 \) and \( \beta_1 \).The regression model to predict the **Price-to-Book Value Ratio** (\( Y \)) based on **Return on Equity** (\( X_1 \)) is:

\[
\hat{Y}_i = 2.3197 + 0.0706 X_{1i}
\]

Where:
- \( 2.3197 \) is the intercept (\( \beta_0 \)).
- \( 0.0706 \) is the slope coefficient for **Return on Equity** (\( \beta_1 \)).

Let me know if you'd like further details or have any questions.

Here are some follow-up questions:
1. How do we interpret the slope in this context?
2. What is the coefficient of determination (\( R^2 \)) for this model?
3. How would you extend the model to include **Growth Percentage** (\( X_2 \))?
4. What assumptions are made in linear regression?
5. How can we test the significance of the coefficients?

**Tip:** The slope tells you how much the **Price-to-Book Value Ratio** is expected to change for a one-unit increase in **Return on Equity**.

A financial analyst engaged in business valuation obtained financial data on 7171 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. Use the accompanying data to complete parts a through e. Part a: Develop a regression model to predict price-to-book-value ratio based on return on equity.

Learn how to develop a regression model to predict price-to-book value ratio based on return on equity. This business valuation problem involves data from drug companies and uses linear regression techniques. Suitable for undergraduate or graduate-level students studying business or finance.

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