True or False: A zero population correlation coefficient between a pair of random variable means that there is no linear relationship between the random variable.
True.
False: A zero population correlation coefficient between a pair of random variables means that there is no linear relationship between the random variables. However, it doesn't necessarily indicate the absence of a non-linear relationship. So, there could still be some wibbly-wobbly, non-linear shenanigans going on between those variables.
False.
A zero population correlation coefficient between a pair of random variables means that there is no linear relationship between the random variables.
True. When the population correlation coefficient between two random variables is zero, it suggests that there is no linear relationship between the variables. In other words, the variables are not linearly related to each other. However, this statement is specifically regarding the population correlation coefficient, not the sample correlation coefficient which is calculated from a sample of data.
To determine the population correlation coefficient, we need to have access to the entire population data. However, in most cases, we only have access to a sample of data. To estimate the population correlation coefficient based on the sample data, we calculate the sample correlation coefficient.
To compute the sample correlation coefficient, you can follow these steps:
1. Collect a random sample of data for the two variables of interest.
2. Calculate the mean (average) of each variable from the sample.
3. Calculate the standard deviation of each variable from the sample.
4. For each data point, calculate the deviation from the mean for both variables.
5. Multiply the deviations obtained in step 4 for each data point.
6. Sum up the results obtained in step 5.
7. Divide the sum from step 6 by the product of the sample standard deviations of the two variables.
8. The result is the sample correlation coefficient.
If the sample correlation coefficient is close to zero or zero, it suggests that there is no or a weak linear relationship between the variables in the sample. However, keep in mind that the sample correlation coefficient might not perfectly represent the population correlation coefficient, so it is important to interpret the result with caution.