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1 results

  • 8 - Linear Regression: Least Squares Estimation

  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book:
    Statistical Methods for Climate Scientists
    Published online:
    03 February 2022
    Print publication:
    24 February 2022, pp 185-209

  • Summary

    Some variables can be modeled by a linear combination of other random variables, plus random noise. Such models are used to quantify the relation between variables, to make predictions, and to test hypotheses about the relation between variables. After identifying the variables to include in a model, the next step is to estimate the coefficients that multiply them, called the regression parameters. This chapter discusses the least squares method for estimating regression parameters. The least squares method estimates the parameters by minimizing the sum of squared differences between the fitted model and the data. This chapter also describes measures for the goodness of fit and an illuminating geometric interpretation of least squares fitting. The least squares method is illustrated on various routine calculations in weather and climate analysis (e.g., fitting a trend). Procedures for testing hypotheses about linear models are discussed in the next chapter.