Statistics pp 54-63 | Cite as

Linear regression

  • P. Sabine
  • C. Plumpton
Part of the Core Books in Advanced Mathematics book series (CBAM)


In the previous chapters we have considered only distributions of a single variable. Each member of the sample had one, and the same, characteristic recorded. For example, we had samples representing populations of times of travel, of heights, and of many other single variables. We now consider populations and samples where each member has the same two particular characteristics recorded; we call this bivariate data, as opposed to the previous univariate data. A sample of bivariate data can be illustrated in a sketch using two perpendicular axes, one axis representing one recorded characteristic, and the other axis representing the other characteristic. For a sample of size n, we can plot the n pairs of recordings on a scatter diagram. For example, below are the data from a sample of 10 healthy women between the ages of 20 and 60 years for whom age (in years) and diastolic blood pressure (in mm of mercury) are recorded.
If one of the two variables has no error in it (in our case “age”) this is the independent variable and we can call this variable x. The other variable will

Fig. 5.1

then be y, the dependent variable (in our case “blood pressure”), depending on x. The variable y is a random variable, each determination of y having a random error involved in its recording. For our example, the scatter diagram is shown in Fig. 5.1.


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Copyright information

© P. Sabine and C. Plumpton 1985

Authors and Affiliations

  • P. Sabine
    • 1
    • 2
  • C. Plumpton
    • 1
    • 3
  1. 1.University of London School Examinations DepartmentUK
  2. 2.Chelsea CollegeUniversity of LondonUK
  3. 3.Queen Mary CollegeUniversity of LondonUK

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