Coefficient of Correlation and Variation Unaccounted For

Definition of Coefficient of Correlation: The coefficient of correlation is a statistical measure that indicates the extent to which two variables are related to each other. It is represented by the symbol 'r' and ranges between -1 to +1.

Formula for Coefficient of Correlation: r = (nΣxy - ΣxΣy) / sqrt[(nΣx² - (Σx)²) * (nΣy² - (Σy)²)]

Interpretation of Coefficient of Correlation: The value of 'r' indicates the strength and direction of the relationship between two variables. If 'r' is close to +1, it means that there is a strong positive correlation between the variables, i.e., as one variable increases, the other variable also increases. If 'r' is close to -1, it means that there is a strong negative correlation between the variables, i.e., as one variable increases, the other variable decreases. If 'r' is close to 0, it means that there is no correlation between the variables.

Formula for Percentage of Variation Unaccounted For: Percentage of variation unaccounted for = (1 - r²) * 100%

Explanation: In this question, the coefficient of correlation between two variables is given as 0.7. This means that there is a strong positive correlation between the variables. Now, we need to find the percentage of variation unaccounted for. This can be done using the formula mentioned above.

Percentage of variation unaccounted for = (1 - r²) * 100%
= (1 - 0.7²) * 100%
= (1 - 0.49) * 100%
= 51%

Therefore, the percentage of variation unaccounted for is 51%. This means that 51% of the variation in one variable is not explained by the variation in the other variable, even though there is a strong positive correlation between them.