Lecture 5: Regression Analysis using Excel and R

Overview

• Focus on linear regression and multilinear regression.
• Tools used: Excel and R.

Using Excel for Regression Analysis

Steps for Linear Regression

1. Setup Data in Excel

   • Copy and paste data using "Copy, Paste Special" to ensure values remain constant.
   • Save the data to avoid random changes.

2. Perform Regression Analysis

   • Navigate to Data > Data Analysis > Regression.
   • Select the Y input range (e.g., column F), and similarly select X input range if needed.
   • Choose additional outputs like residuals and residual plots.

3. Interpret Results

   • R-Square Value: Indicates the model's fit.
   • Intercept Values: Part of the linear equation of the model.
   • T-Test: Checks if coefficients are significantly different from zero.
   • P-Value: Interpret to understand the significance level.
   • Confidence Intervals: Estimate range for the intercept value.
   • F-Test: Tests the interaction between variables.

Challenges

• Large datasets might crash Excel.
• Sample data should be used for smoother analysis.

Using R for Regression Analysis

Setting Up RStudio

1. Importing Data
   • Use Import from Excel feature to load dataset.
2. Create Linear Model
   • Use lm() function: lm(value ~ cost, data = UNData).
   • Check syntax and ensure correct variable names are used (case sensitive).

Interpreting R Output

• Coefficients and Intercept: Extracted from the lm model.
• Residuals vs Fitted Plot: Used to check heteroscedasticity.
  • Homoscedasticity: Uniform distribution of residual points.
  • Heteroscedasticity: Cone-shaped residuals and a sloping red line, indicates variance in error terms.

Key Concepts

• Homoscedasticity: Equal variance in the data; a good fit for regression.
• Heteroscedasticity: Unequal variance; problematic for regression interpretation.

Summary

• Overview of how to conduct regression analysis using both Excel and R.
• Considerations for choosing tools based on dataset size and functionality.
• Brief introduction to linear regression concepts and checks for validity.

Conclusion

• Presumed familiarity with basic regression concepts.
• This serves as an introduction, with deeper exploration encouraged in both Excel and R environments.