Math Problem Statement

data-9_24_2024-1_29 PM.xlsx

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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.)

Solution

The data includes three columns:

  1. Price-to-Book Value Ratio (dependent variable, YY)
  2. Return on Equity (independent variable X1X_1)
  3. Growth Percentage (independent variable X2X_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 (X1X_1).

The regression model will be in the form: Y^i=β0+β1X1i\hat{Y}_i = \beta_0 + \beta_1 X_{1i} We'll compute the coefficients β0\beta_0 and β1\beta_1.The regression model to predict the Price-to-Book Value Ratio (YY) based on Return on Equity (X1X_1) is:

Y^i=2.3197+0.0706X1i\hat{Y}_i = 2.3197 + 0.0706 X_{1i}

Where:

  • 2.31972.3197 is the intercept (β0\beta_0).
  • 0.07060.0706 is the slope coefficient for Return on Equity (β1\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 (R2R^2) for this model?
  3. How would you extend the model to include Growth Percentage (X2X_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.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Statistics
Business Valuation

Formulas

Y = β0 + β1 * X1

Theorems

Ordinary Least Squares (OLS) Regression

Suitable Grade Level

Undergraduate/Graduate