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
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A company is interested in determining the strength of association between the
communication time of their employees and the level of stress-related problems observed
on job. A study of 120 assembly line workers reveals the following data:
|
| Stress | |||
|
| High | Moderate | Low | Total |
| Under 20 min | 10 | 10 | 15 | 35 |
| 20- 50 min | 15 | 10 | 25 | 50 |
| Over 50 min | 15 | 10 | 10 | 35 |
| Total | 40 | 30 | 50 | 120 |
Write the properties Of a good measure Of dispersion. The following information for the two groups of individuals is given as:
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 |
The arithematic mean of n natural numbers assinged the values 1, 2, 3,.....,n is 
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 |
For the following distribution, calculate first four central moments using recurrence
relations. Also find the coefficients of skewness and kurtosis.
| Marks: | 2.7- 7.5 | 7.5- 12.5 | 12.5- 17.5 | 17.5- 22.5 | 22.5- 27.5 | 27.5- 32.5 | 32.5- 37.5 |
| Frequency: | 06 | 13 | 23 | 39 | 19 | 15 | 05 |
