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3: Introduction to Linear Regression and Correlation

  • Page ID
    26043
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    Regression analysis is a statistical process for estimating the relationships among variables and includes many techniques for modeling and analyzing several variables. When the focus is on the relationship between a dependent variable and one or more independent variables.

    • 3.1: Linear Equations
      Linear regression for two variables is based on a linear equation with one independent variable. The equation has the form: y=a+bx where a and b are constant numbers. The variable x is the independent variable, and y is the dependent variable. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.
    • 3.2: Scatter Plots
      A scatter plot shows the direction of a relationship between the variables. A clear direction happens when there is either: High values of one variable occurring with high values of the other variable or low values of one variable occurring with low values of the other variable. High values of one variable occurring with low values of the other variable.
    • 3.3: Simple Linear Regression
      A regression line, or a line of best fit, can be drawn on a scatter plot and used to predict outcomes for the x and y variables in a given data set or sample data. There are several ways to find a regression line, but usually the least-squares regression line is used because it creates a uniform line. Residuals measure the distance from the actual value of y and the estimated value of y . The Sum of Squared Errors, when set to its minimum, calculates the points on the line of best fit.
    • 3.4: Prediction
      After determining the presence of a strong correlation coefficient and calculating the line of best fit, you can use the least squares regression line to make predictions about your data.  The process of predicting inside of the observed x values observed in the data is called interpolation. The process of predicting outside of the observed x-values observed in the data is called extrapolation.
    • 3.5: Outliers
      In some data sets, there are values (observed data points) called outliers. Outliers are observed data points that are far from the least squares line. They have large "errors", where the "error" or residual is the vertical distance from the line to the point.

    Contributors and Attributions

    • Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/30189442-699...b91b9de@18.114.


    This page titled 3: Introduction to Linear Regression and Correlation is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.