Regression and Correlation Concepts

Key Concepts

• Regression analyzes the relationship between paired sample data points.

• The best-fitting line is termed the regression line, represented by a regression equation.

Regression Line

• The regression line (also known as line of best fit or least-squares line) best fits the scatterplot of paired data.

Regression Equation

• The regression equation is expressed as $y = mx + b$.

  • $x$: explanatory (predictor) variable.

  • $y$: response (dependent) variable.

• The TI-83/84 calculator's LinReg(ax+b) function provides this equation.

Making Predictions

1. Bad Model: Avoid predictions with a regression equation if it doesn't fit the data; use the sample mean instead.

2. Good Model: Ensure the regression line fits the scatterplot well before using it for predictions.

3. Correlation: The linear correlation coefficient $r$ must indicate correlation between the variables to use the regression equation for predictions.

4. Scope: Only make predictions within the range of the sample data.

Residual

• The residual represents the difference between the observed value of $y$ and the predicted value from the regression equation.