70.1k views
1 vote
Features of coefficient of correlation between sample and population are:

A) Always positive and equal
B) Always negative and equal
C) Not necessarily equal, sample correlation tends to underestimate population correlation
D) Not necessarily equal, sample correlation tends to overestimate population correlation

User TheYann
by
7.4k points

1 Answer

4 votes

Final answer:

The sample correlation coefficient, r, is not necessarily equal to the population correlation coefficient and tends to underestimate the population correlation.

Step-by-step explanation:

The correct answer to the question 'Features of coefficient of correlation between sample and population are' is: C) Not necessarily equal, sample correlation tends to underestimate population correlation.

The correlation coefficient, represented by the letter r, is a statistical measure that calculates the strength and direction of a linear relationship between two variables. The values of r range from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship at all. The sign of the correlation coefficient indicates whether there is a positive or negative linear relationship between the variables.

When dealing with sample data, the sample correlation coefficient 'r' is used as an estimate of the true population correlation coefficient. Due to various factors such as sample size and sampling error, the sample correlation coefficient may not be equal to the actual population correlation coefficient. Furthermore, it is often the case that the sample correlation underestimates the population correlation due to a phenomenon known as regression dilution or attenuation. This should not be confused with overestimating the population correlation.

User Mrimsh
by
7.6k points