Describe the assumptions for correlation Prove that correlation coefficient is independent
of change of origin and scale both.
1. Assumptions for Correlation:
Correlation is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. Several assumptions are important when dealing with correlation:
a. Linearity: The relationship between the two variables should be approximately linear. Correlation is primarily designed to measure linear associations, so if the relationship is nonlinear, correlation may not accurately reflect the association.
b. Independence: The observations of the two variables should be independent of each other. In other words, the value of one variable should not depend on the value of the other. Violation of this assumption can lead to spurious correlations.
c. Homoscedasticity: The variances of the two variables should be roughly constant across different values of the variables. In cases of heteroscedasticity (varying variances), correlation may be affected.
d. Outliers: Extreme values or outliers can unduly influence the correlation
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Calculate the rank correlation coefficient for the following data:
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Mathematics | 76 | 80 | 85 | 80 | 78 | 65 | 85 | 80 |
| Physics | 91 | 78 | 82 | 78 | 86 | 80 | 88 | 92 |
Why are two different lines of regression used to obtain the optimum values of two
variables X and Y. The marks of lo students of a class in Mathematics and Statistics are given below:
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mathematics | 40 | 46 | 42 | 30 | 35 | 28 | 39 | 43 | 25 | 45 |
| Statistics | 35 | 41 | 36 | 32 | 42 | 48 | 29 | 38 | 28 | 40 |
Describe the conditions for consistency of the data. In a sample of 1000 students admitted
in a college, 500 belonged to rural areas and the rest belonged to urban areas. The number
of students belonging CBSE Board from both areas are 200 and 100, respectively.
Calculate the coefficient of association between area and the Board of Education.
Calculate the first, second and third quartile for following data:
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 05 | 15 | 30 | 12 | 08 |
The correlation coefficient between two variables X and Y, 
Describe the assumptions for correlation Prove that correlation coefficient is independent
of change of origin and scale both.