Linear Correlation and Modeling

Key Questions

  • What is the range of possible values of a correlation coefficient?

    The possible values of the correlation coefficient are, #-1<=r<=1#.

    An #r# value near #1# indicates a positive correlation.
    An #r# value near #-1# indicates a negative correlation.
    An #r# value near #0# indicates no correlation.

    AJ Speller · 6 · Sep 14 2014
  • How do I find and interpret the linear correlation coefficient?

    Answer:

    See explanation. I would suggest that you look it up in a book. Dictionary of mathematics perhaps.

    Explanation:

    #color(blue)("Finding the coefficient")#

    This is one of those questions that is rather like: "how long is a piece of string".

    It all depends on the structure of the relationship which has many variations. So it is hard to give a definitive answer.

    Linea points to a fixed value coefficient.

    By example:

    Let the independent variable be #x#
    Let the dependant variable be #y#
    Let the correlation coefficient be #k#

    Then we have the general form of;

    #y=kx#

    To find the value of #k# divide both sides by #x# giving:

    #k=y/x#
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    #color(blue)("Interpreting the coefficient")#

    Again this is dependant on context. Basically it fixes the major relationship between the dependant and independent variables.

    It could be described as a conversion factor

    Tony B · 1 · Jan 2 2017

Questions

Linear and Quadratic Functions