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:
- Price-to-Book Value Ratio (dependent variable, )
- Return on Equity (independent variable )
- Growth Percentage (independent variable , 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 ().
The regression model will be in the form: We'll compute the coefficients and .The regression model to predict the Price-to-Book Value Ratio () based on Return on Equity () is:
Where:
- is the intercept ().
- is the slope coefficient for Return on Equity ().
Let me know if you'd like further details or have any questions.
Here are some follow-up questions:
- How do we interpret the slope in this context?
- What is the coefficient of determination () for this model?
- How would you extend the model to include Growth Percentage ()?
- What assumptions are made in linear regression?
- 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
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