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:

  1. Price/Book Value Ratio: The target variable we need to predict.
  2. Return on Equity: Independent variable X1X_1.
  3. Growth%: Independent variable X2X_2.

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 (Yi^\hat{Y_i}) based on Return on Equity (X1iX_{1i}) and Growth (X2iX_{2i}) is given by the equation:

Yi^=1.941+0.0598X1i+0.022X2i\hat{Y_i} = 1.941 + 0.0598 \cdot X_{1i} + 0.022 \cdot X_{2i}

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:

  1. How accurate is this model in predicting Price-to-Book Value Ratio?
  2. What is the R-squared value for this regression model?
  3. Can we test the significance of each predictor variable?
  4. How do we interpret the coefficients in a practical business context?
  5. 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