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If the coefficient of correlation between two variables is 0.6, then the percentage of variation unaccounted for is
- a)60%
- b)40%
- c)64%
- d)36%
Correct answer is option 'C'. Can you explain this answer?
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If the coefficient of correlation between two variables is 0.6, then t...
Explanation:
The coefficient of correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative relationship, +1 indicates a perfect positive relationship, and 0 indicates no relationship.
In this question, the coefficient of correlation between two variables is 0.6, which indicates a moderate positive relationship between the variables. It means that as one variable increases, the other variable also tends to increase, but not necessarily at the same rate.
Percentage of variation unaccounted for:
The coefficient of correlation only measures the linear relationship between two variables. It does not tell us anything about the amount of variation in one variable that can be explained by the other variable. To calculate the percentage of variation unaccounted for, we need to square the coefficient of correlation and subtract it from 1.
Percentage of variation unaccounted for = (1 - r^2) x 100%
Where r is the coefficient of correlation.
In this question, the coefficient of correlation is 0.6, so the percentage of variation unaccounted for is:
(1 - 0.6^2) x 100% = 1 - 0.36 x 100% = 64%
Therefore, option C, 64%, is the correct answer. It means that 64% of the variation in one variable is not explained by the other variable. The remaining 36% is accounted for by the linear relationship between the variables.
The coefficient of correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative relationship, +1 indicates a perfect positive relationship, and 0 indicates no relationship.
In this question, the coefficient of correlation between two variables is 0.6, which indicates a moderate positive relationship between the variables. It means that as one variable increases, the other variable also tends to increase, but not necessarily at the same rate.
Percentage of variation unaccounted for:
The coefficient of correlation only measures the linear relationship between two variables. It does not tell us anything about the amount of variation in one variable that can be explained by the other variable. To calculate the percentage of variation unaccounted for, we need to square the coefficient of correlation and subtract it from 1.
Percentage of variation unaccounted for = (1 - r^2) x 100%
Where r is the coefficient of correlation.
In this question, the coefficient of correlation is 0.6, so the percentage of variation unaccounted for is:
(1 - 0.6^2) x 100% = 1 - 0.36 x 100% = 64%
Therefore, option C, 64%, is the correct answer. It means that 64% of the variation in one variable is not explained by the other variable. The remaining 36% is accounted for by the linear relationship between the variables.
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If the coefficient of correlation between two variables is 0.6, then the percentage of variation unaccounted for isa)60%b)40%c)64%d)36%Correct answer is option 'C'. Can you explain this answer?
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