For an experiment we have the following data set: n = 4, ∑x = a, ∑y = 10, ∑xy = 21, ∑x2 = 30, ∑y2 = 30. If the correlation coefficient is -0.8 then the value of a is:

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SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )
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  1. 7
  2. 10
  3. 8
  4. 9

Answer (Detailed Solution Below)

Option 2 : 10
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Detailed Solution

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The correct answer is 10.

Key Points

  • The correlation coefficient only measures linear relationships, so it does not necessarily indicate causality.
  • The value of a in this data set only represents the sum of the x values and does not necessarily have a specific meaning in the context of the experiment.
  •  The value of a in the data set is 10.
  • The correlation coefficient of -0.8 indicates a strong negative linear relationship between the two variables, x and y.
  • This information along with the other statistics provided can be used to calculate a using statistical formulas.

Additional Information 

  • The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables.
  • A correlation of -1 indicates a perfect negative linear relationship, while a correlation of 1 indicates a perfect positive linear relationship.
  • The formula to calculate the correlation coefficient is: r = (n∑xy - ∑x∑y) / (√(n∑x2 - (∑x)^2) * √(n∑y2 - (∑y)^2))
  • In this case, we know the value of r (-0.8), so we can rearrange the formula and solve for a.

 

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