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Q. If the coefficient of correlation between two variables is –0 9, then the coefficient of determination is
  • a)
    0.9
  • b)
    0.81
  • c)
    0.1
  • d)
    0.19
Correct answer is 'B'. Can you explain this answer?
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Coefficient of Correlation and Determination

Coefficient of correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.

Coefficient of determination, on the other hand, measures the proportion of the total variation in one variable that can be explained by the variation in the other variable. It ranges from 0 to 1, where 0 represents no relationship, and 1 represents a perfect relationship.

Calculation of Coefficient of Determination

The coefficient of determination is calculated by squaring the coefficient of correlation. Therefore, if the coefficient of correlation between two variables is 0.9, then the coefficient of determination will be:

Coefficient of determination = (0.9)2 = 0.81

Interpretation of Coefficient of Determination

The coefficient of determination represents the percentage of the total variation in one variable that is explained by the variation in the other variable. In this case, since the coefficient of determination is 0.81, it means that 81% of the total variation in one variable is explained by the variation in the other variable.

Conclusion

Therefore, the correct answer to the question is B, i.e., 0.81, since the coefficient of determination is calculated by squaring the coefficient of correlation.
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0:81
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(Direction 1 - 2) Write the correct answers. Each question carries 1 mark.Q.If the coefficient of correlation between two variables is –0 9, then the coefficient of determination isa)0.9b)0.81c)0.1d)0.19Correct answer is 'B'. Can you explain this answer?
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