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If the coefficient of correlation between two variables is 0.7 then the percentage of variation unaccounted for is
- a)70%
- b)30%
- c)51%
- d)49%
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the coefficient of correlation between two variables is 0.7 then th...
Coefficient of Correlation:
The coefficient of correlation is a statistical measure that shows the degree of association between two variables. It ranges from -1 to +1. A value of +1 indicates a perfect positive correlation, while a value of -1 indicates a perfect negative correlation. A value of 0 indicates no correlation between the variables.
Calculation of Unaccounted Variation:
The coefficient of correlation measures the degree of association between two variables. It does not measure the amount of variation between the variables. The amount of variation between two variables is measured by the coefficient of determination, which is the square of the coefficient of correlation.
The coefficient of determination (R^2) is calculated as follows:
R^2 = (Coefficient of Correlation)^2
Therefore, if the coefficient of correlation is 0.7, the coefficient of determination is:
R^2 = 0.7^2 = 0.49
The coefficient of determination represents the proportion of the total variation in one variable that is accounted for by the other variable. Therefore, the percentage of variation unaccounted for is:
Percentage of variation unaccounted for = (1 - R^2) x 100
= (1 - 0.49) x 100
= 51%
Therefore, the correct answer is option C, which is 51%.
The coefficient of correlation is a statistical measure that shows the degree of association between two variables. It ranges from -1 to +1. A value of +1 indicates a perfect positive correlation, while a value of -1 indicates a perfect negative correlation. A value of 0 indicates no correlation between the variables.
Calculation of Unaccounted Variation:
The coefficient of correlation measures the degree of association between two variables. It does not measure the amount of variation between the variables. The amount of variation between two variables is measured by the coefficient of determination, which is the square of the coefficient of correlation.
The coefficient of determination (R^2) is calculated as follows:
R^2 = (Coefficient of Correlation)^2
Therefore, if the coefficient of correlation is 0.7, the coefficient of determination is:
R^2 = 0.7^2 = 0.49
The coefficient of determination represents the proportion of the total variation in one variable that is accounted for by the other variable. Therefore, the percentage of variation unaccounted for is:
Percentage of variation unaccounted for = (1 - R^2) x 100
= (1 - 0.49) x 100
= 51%
Therefore, the correct answer is option C, which is 51%.
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Community Answer
If the coefficient of correlation between two variables is 0.7 then th...
R=0.7
r^=?
then
0.7×0.7=0.49
0.49×100=49%
49%is accounted
so 100%-49%=51%
r^=?
then
0.7×0.7=0.49
0.49×100=49%
49%is accounted
so 100%-49%=51%
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If the coefficient of correlation between two variables is 0.7 then the percentage of variation unaccounted for isa)70%b)30%c)51%d)49%Correct answer is option 'C'. Can you explain this answer?
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