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Linear Regression & Least Squares Method definitions

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  • Scatter Plot
    Graphical display showing the relationship between two variables using plotted points on x and y axes.
  • Correlation
    Measure indicating the strength and direction of a relationship between two variables in a dataset.
  • Linear Regression
    Statistical technique modeling the relationship between two variables with a straight line equation.
  • Least Squares Method
    Procedure for finding the line that minimizes the sum of squared vertical distances from data points.
  • Residual
    Vertical distance between a data point and the predicted value on the regression line.
  • Best Fit Line
    Line that most closely represents the trend in the data, minimizing the sum of squared residuals.
  • Regression Equation
    Formula, typically y=ax+b, used to predict values based on the linear relationship between variables.
  • Slope
    Rate of change in the regression equation, indicating how much y changes for each unit increase in x.
  • Y-Intercept
    Value where the regression line crosses the y-axis, representing predicted y when x is zero.
  • Extrapolation
    Prediction for values outside the observed data range, often less reliable than within-range estimates.
  • Mean
    Average value of a dataset, used as the best estimate when predictions fall outside the data range.
  • Linear Correlation Coefficient
    Numerical value, often r, quantifying the strength and direction of linear association between variables.
  • Stat Plot
    Calculator feature enabling visualization of data points for analysis of patterns and trends.
  • Diagnostic On
    Calculator setting that activates statistical diagnostics, including correlation coefficients.
  • Y Hat
    Symbol representing predicted values from the regression equation, distinguishing them from actual data.