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LINEAR CORRELATION — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsLINEAR CORRELATION3 Marks
Question
State the necessary precautions to be taken while interpreting the value of correlation coefficient.
✓

Answer

  • The coefficient of correlation measures the strength of linear relationship between two variables.
  • The following are some of the points to be kept in mind as precaution to interpret it carefully :
  • $(1)$ Spurious Correlation :
    • The value of correlation coefficient I does not indicate any cause effect relation or any meaningful relation between two variables.
    • In many cases there is no meaningful relation but value of correlation coefficient I calculated on the basis of observations of two variables comes very near to $1.$
    • For example there is no meaningful relation between America's per capita income and number of deaths caused due to cancer in India but still if we calculate correlation coefficient r between them by taking observations during a particular time, its value will be near $1.$
    • In such cases there is no cause effect relation between two variables $X$ and $Y$ also the increase or decrease in their values are due to other factors.
    • Therefore it is wrong to interpret that the two variables are correlated or not correlated on the basis of value of correlation coefficient r.
  • $(2)$ Lack of Correlation :
    • It is wrong to interpret that there is no correlation between two random variables $X$ and $Y$ when the value of coefficient of correlation is $0 ($zero$).$
    • In such cases it can be said that there is lack of linear correlation between two random variables $X$ and $Y.$
  • $(3)$ Interpretation of value of correlation coefficient :
    • If the correlation coefficient is computed from the data which is related to a given region or class or given time duration then its interpretation should be limited to that region or Class or time duration only.
    • The interpretation of such correlation coefficient should not be extended or generalised outside the region, class or time without proper verification in order to avoid any kind of misunderstanding.

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