Lecture Notes: Introduction to Regression Analysis

Course Overview

• Course Code: SD501
• Objective: Gain an in-depth understanding of select topics, focusing on regression analysis.
• Comparison to SD500: Unlike the survey approach in SD500, SD501 focuses deeper on fewer topics.
• First Project: Regression analysis project due in about two weeks.
• Course Environment: Emphasis on reducing stress and anxiety.

Regression Analysis

• Definition: Regression, also known as best-fit or fit analysis, is moving towards the average value of the data.
• Purpose: To model and predict relationships between variables.

Understanding Regression Modeling

• Terminology:
  • Regression Line: Represents the average direction of data.
  • Regression Equation: Moves toward the mean.
• Model Types:
  • Different potential models can be considered, analyzed for the best fit.

Sample Selection for Large Data Sets

• Guideline: Use a sample size = 10% of population or max 1,000, to avoid computational strain.
• Reason: Manage computational resources efficiently.

Anova Table

• Definition: Used in regression analysis to evaluate variance.
• Analysis of Variance (ANOVA): Examines differences from the mean.

Hypothesis in Regression

• Null Hypothesis (H0): Model explains none of the variability.
• Alternative Hypothesis (H1): Model explains some of the variability.
• Example: Regression model predicts outcomes based on independent predictor variables.

Components of Anova Analysis

• F Statistic: Ratio of mean regression sum of squares to mean error sum of squares.
• Sum of Squares:
  • Total Sum of Squares (TSS): Total variance in data.
  • Regression Sum of Squares (RSS): Variance explained by the model.
  • Error Sum of Squares (ESS): Variance not explained by the model.
• Mean Square Values: Average variance per data point.

Degrees of Freedom

• Definition: Number of values free to vary in calculations.
• Past Relevance: Used for looking up values in statistical tables.

P Value

• Importance: Determines statistical significance.
• Threshold: Typically <= 0.05 for significance.
• Interpretation:
  • Low P value suggests rejecting the null hypothesis.
  • High P value suggests retaining the null hypothesis.

Modern Implications

• Role of Technology: Computers handle complex calculations, making manual reference less critical.
• Practical Application: Understanding terms is crucial for executing regression modeling projects.

Next Steps

• Topics to Cover: Multiple R and R squared, further example analysis.
• Break: Lecture paused for a short break.