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The correlation coefficient (r) between two variables is 0.9. The unexplained variation (%) is ______________
(Important - Enter only the numerical value in the answer)
Correct answer is '19'. Can you explain this answer?
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The correlation coefficient (r) between two variables is 0.9. The unex...
The correlation coefficient (r) between two variables measures the strength and direction of the linear relationship between them. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no linear correlation.
To calculate the unexplained variation, we need to understand the concept of explained variation first.
Explained variation is the proportion of the total variation in one variable that can be explained by the linear relationship with the other variable. It is calculated by squaring the correlation coefficient (r) and multiplying it by 100. In other words, it represents the percentage of the variation in one variable that is accounted for by the other variable.
So, the formula for explained variation is:
Explained Variation = (r^2) * 100
Given that the correlation coefficient (r) between the two variables is 0.9, we can calculate the explained variation as follows:
Explained Variation = (0.9^2) * 100 = 0.81 * 100 = 81%
Now, to calculate the unexplained variation, we subtract the explained variation from 100%:
Unexplained Variation = 100% - Explained Variation = 100% - 81% = 19%
Therefore, the unexplained variation is 19%.
This means that 19% of the total variation in one variable cannot be explained by the linear relationship with the other variable. It represents the random or unpredictable part of the variation that is not accounted for by the correlation between the two variables.
To calculate the unexplained variation, we need to understand the concept of explained variation first.
Explained variation is the proportion of the total variation in one variable that can be explained by the linear relationship with the other variable. It is calculated by squaring the correlation coefficient (r) and multiplying it by 100. In other words, it represents the percentage of the variation in one variable that is accounted for by the other variable.
So, the formula for explained variation is:
Explained Variation = (r^2) * 100
Given that the correlation coefficient (r) between the two variables is 0.9, we can calculate the explained variation as follows:
Explained Variation = (0.9^2) * 100 = 0.81 * 100 = 81%
Now, to calculate the unexplained variation, we subtract the explained variation from 100%:
Unexplained Variation = 100% - Explained Variation = 100% - 81% = 19%
Therefore, the unexplained variation is 19%.
This means that 19% of the total variation in one variable cannot be explained by the linear relationship with the other variable. It represents the random or unpredictable part of the variation that is not accounted for by the correlation between the two variables.
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Community Answer
The correlation coefficient (r) between two variables is 0.9. The unex...
Square of 0.9 is 0.81(81%)
100%-81% = 19%
100%-81% = 19%
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The correlation coefficient (r) between two variables is 0.9. The unexplained variation (%) is______________(Important - Enter only the numerical value in the answer)Correct answer is '19'. Can you explain this answer?
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