Math Problem Statement
data-9_24_2024-12_57 PM.xlsx
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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
enter your response hereplus
enter your response hereUpper X Subscript 1 iplus
enter your response hereUpper X Subscript 2 i (Round to four decimal places as needed.)
Solution
The dataset contains the following columns:
- Price/Book Value Ratio: The target variable we need to predict.
- Return on Equity: Independent variable .
- Growth%: Independent variable .
I will now develop a regression model to predict the Price-to-Book Value Ratio using these two predictors. Let's calculate the coefficients and intercept of the regression equation.The regression model to predict the Price-to-Book Value Ratio () based on Return on Equity () and Growth () is given by the equation:
This equation suggests:
- For each additional unit increase in Return on Equity, the Price-to-Book Value Ratio increases by approximately 0.0598 units, holding Growth constant.
- For each additional unit increase in Growth, the Price-to-Book Value Ratio increases by approximately 0.022 units, holding Return on Equity constant.
Would you like more details or have any questions about this model?
Here are 5 related questions to consider:
- How accurate is this model in predicting Price-to-Book Value Ratio?
- What is the R-squared value for this regression model?
- Can we test the significance of each predictor variable?
- How do we interpret the coefficients in a practical business context?
- Are there any outliers or influential points that affect the model?
Tip: When interpreting regression coefficients, consider the scale and unit of each variable to understand their impact accurately.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Predictive Modeling
Statistics
Formulas
Y = β0 + β1 * X1 + β2 * X2
R-squared = 1 - (Σ(y_i - ŷ_i)^2 / Σ(y_i - ȳ)^2)
Theorems
Ordinary Least Squares (OLS)
Coefficient of Determination (R-squared)
Suitable Grade Level
Undergraduate/Graduate Level
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