Math Problem Statement

data-9_24_2024-12_40 PM.xlsx

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a. Develop a regression model to predict​ price-to-book-value ratio based on return on equity. ModifyingAbove Upper Y with caret Subscript iequals

enter your response hereplus

enter your response hereUpper X Subscript 1 i ​(Round to four decimal places as​ needed.)

Solution

The dataset consists of three columns:

  1. Price/Book Value Ratio
  2. Return on Equity
  3. Growth%

To develop the regression model that predicts the Price/Book Value Ratio based on the Return on Equity, we will fit a simple linear regression model. I will proceed with the regression and round the coefficients to four decimal places.The linear regression model to predict the Price-to-Book Value Ratio based on Return on Equity is:

Y^i=2.3328+0.0700X1i\hat{Y}_i = 2.3328 + 0.0700 X_{1i}

Where:

  • Y^i\hat{Y}_i is the predicted Price-to-Book Value Ratio.
  • X1iX_{1i} is the Return on Equity.

Would you like further details on the regression analysis, or do you have any questions?

Here are 5 related questions for deeper exploration:

  1. How does the model's accuracy compare to other possible predictors?
  2. Can we add the Growth% variable to improve the model's performance?
  3. How do we interpret the coefficient of the model in practical terms?
  4. What assumptions are we making when using linear regression here?
  5. Can we use this model for future predictions if new data is available?

Tip: Always check the residuals of the model to ensure that the linearity assumption holds.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Predictive Modeling
Statistics

Formulas

Simple Linear Regression Formula: Y = β0 + β1X

Theorems

Ordinary Least Squares (OLS) Method

Suitable Grade Level

College/University