14.6 Use of R Statistical Analysis Tool for Regression Analysis

R for regression analysis in finance empowers investors to uncover relationships between financial variables. From correlation coefficients to linear regression models, R provides tools to measure and visualize connections between stock returns, market performance, and other economic factors.

Interpreting R output helps predict financial outcomes and assess model reliability. By understanding coefficients, p-values, and R-squared metrics, investors can make data-driven decisions and evaluate the strength of their predictive models in the ever-changing financial landscape.

R for Regression Analysis in Finance

Correlation coefficients in finance

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  Spearman's rank correlation coefficient - Wikipedia View original

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  CSUP Math 156 Correlation and Linear Regression View original

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• Measure the strength and direction of the linear relationship between two variables (stock returns and market returns)
  • Range from -1 to 1
    • -1 perfect negative linear relationship (as one variable increases, the other decreases proportionally)
    • 0 no linear relationship (changes in one variable have no impact on the other)
    • 1 perfect positive linear relationship (as one variable increases, the other increases proportionally)
• Calculate using the

  [cor()](https://www.fiveableKeyTerm:cor())

  function in R
  • Syntax:

    cor(x, y)

    • x

      and

      y

      vectors containing the financial variables (stock prices and earnings per share)
  • Example:

    cor(stock_returns, market_returns)

    calculates the correlation between stock returns and market returns
• Visualize relationships between variables using scatter plots (data visualization)

Linear regression for financial metrics

• Models the relationship between a dependent variable and one or more independent variables
  • Dependent variable (Y) the variable being predicted or explained (stock price)
  • Independent variable(s) (X) the variables used to predict or explain the dependent variable (earnings per share and debt-to-equity ratio)
• Create linear regression models using the

  [lm()](https://www.fiveableKeyTerm:lm())

  function in R
  • Syntax:

    lm(formula, data)

    • formula

      specifies the relationship between the dependent and independent variables (stock_price ~ earnings_per_share)

    • data

      the data frame containing the variables (financial_metrics)
  • Example:

    model <- lm(stock_returns ~ market_returns, data = financial_data)

    creates a linear regression model with stock returns as the dependent variable and market returns as the independent variable
• Multiple linear regression includes more than one independent variable
  • Syntax:

    lm(Y ~ X1 + X2 + ... + Xn, data)

  • Example:

    model <- lm(stock_returns ~ market_returns + interest_rates, data = financial_data)

    creates a multiple linear regression model with stock returns as the dependent variable and market returns and interest rates as independent variables

Interpreting R output for predictions

• View the results of a linear regression model using the

  [summary()](https://www.fiveableKeyTerm:summary())

  function
  • Provides coefficients, standard errors, t-values, and p-values for each independent variable
  • Indicates the overall model fit with metrics like R-squared and adjusted R-squared
    • R-squared the proportion of variance in the dependent variable explained by the independent variable(s)
    • Adjusted R-squared adjusts for the number of independent variables in the model
• Coefficients represent the change in the dependent variable for a one-unit change in the independent variable, holding other variables constant
  • Interpret the sign and magnitude of coefficients to understand the relationship between variables (a coefficient of 1.5 for earnings per share indicates that a $1 increase in earnings per share is associated with a$1.50 increase in stock price)
• P-values indicate the statistical significance of each independent variable
  • A small p-value (typically < 0.05) suggests that the independent variable has a significant impact on the dependent variable
• Make predictions by plugging in values for the independent variable(s)
  • Syntax:

    predict(model, newdata)

    • model

      the linear regression model object

    • newdata

      a data frame containing the values for the independent variable(s) for which you want to make predictions
  • Example:

    predict(model, newdata = data.frame(market_returns = 0.05))

    predicts stock returns when market returns are 5%

Model Diagnostics and Assumptions

• Conduct hypothesis testing to assess the significance of regression coefficients
• Perform residual analysis to check model assumptions and identify potential issues
• Test for multicollinearity among independent variables to ensure reliable coefficient estimates
• Check for heteroscedasticity to validate the consistency of error variance across predictions