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Statistics LibreTexts

7: Introduction to Linear Regression

Linear regression is a very powerful statistical technique. Many people have some familiarity with regression just from reading the news, where graphs with straight lines are overlaid on scatterplots. Linear models can be used for prediction or to evaluate whether there is a linear relationship between two numerical variables.

  • 7.0: Prelude to Linear Regression
    Imagine what a perfect linear relationship would mean: you would know the exact value of y just by knowing the value of x. This is unrealistic in almost any natural process. For example, if we took family income x, this value would provide some useful information about how much financial support y a college may offer a prospective student. However, there would still be variability in financial support, even when comparing students whose families have similar financial backgrounds.
  • 7.1: Line Fitting, Residuals, and Correlation
    In this section, we examine criteria for identifying a linear model and introduce a new statistic, correlation.
  • 7.2: Fitting a Line by Least Squares Regression
    Fitting linear models by eye is open to criticism since it is based on an individual preference. In this section, we use least squares regression as a more rigorous approach.
  • 7.3: Types of Outliers in Linear Regression
    In this section, we identify criteria for determining which outliers are important and influential. Outliers in regression are observations that fall far from the "cloud" of points. These points are especially important because they can have a strong influence on the least squares line.
  • 7.4: Inference for Linear Regression
    In this section we discuss uncertainty in the estimates of the slope and y-intercept for a regression line. Just as we identi ed standard errors for point estimates in previous chapters, we first discuss standard errors for these new estimates. However, in the case of regression, we will identify standard errors using statistical software.
  • 7.5: Exercises
    Exercises for Chapter 7 of the "OpenIntro Statistics" textmap by Diez, Barr and Çetinkaya-Rundel.

Contributors

David M Diez (Google/YouTube), Christopher D Barr (Harvard School of Public Health), Mine Çetinkaya-Rundel (Duke University)