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Linear Regression & Least Squares Method definitions

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  • Scatter Plot
    A graphical display showing paired x and y values, used to visually assess patterns or trends between two variables.
  • Correlation
    A measure indicating the strength and direction of a linear relationship between two variables in a dataset.
  • Least Squares Regression
    A method for determining the best fit line by minimizing the sum of squared vertical distances from data points to the line.
  • Best Fit Line
    A straight line that most closely approximates the data in a scatter plot, found using regression techniques.
  • Residual
    The vertical distance between an observed data point and the value predicted by the regression line.
  • Regression Equation
    An algebraic expression, typically y = ax + b, representing the best fit line for predicting y from x.
  • Slope
    The coefficient of x in the regression equation, indicating the rate of change in y for each unit increase in x.
  • Y-intercept
    The constant term in the regression equation, representing the predicted value of y when x equals zero.
  • Extrapolation
    The process of predicting values outside the observed data range, often less reliable than predictions within the range.
  • Mean
    The arithmetic average of a set of values, used as the best estimate when predictions fall outside the data range.
  • Linear Regression
    A statistical technique for modeling the relationship between two variables with a straight line.
  • Diagnostic On
    A calculator setting that enables display of statistical measures, such as correlation coefficients, during regression analysis.
  • Stat Plot
    A calculator feature that visually displays data points on a graph, aiding in regression and correlation analysis.
  • Correlation Coefficient
    A numerical value, often denoted as r, quantifying the strength and direction of a linear relationship between variables.
  • Y-hat
    The symbol representing predicted y values from the regression equation, distinguishing them from observed values.