X;9, 3, 7, 11, 6. Y;11, 2, 15, 4, 9. Whats the value. The strength. Direction and shared varience
To find the value, strength, direction, and shared variance between variables X and Y, you can perform a correlation analysis. Let's go through the steps:
Step 1: Calculate the correlation coefficient.
The correlation coefficient measures the strength and direction of the relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative relationship, 1 indicates a perfect positive relationship, and 0 indicates no relationship.
Using a statistical software or calculator, calculate the correlation coefficient (also known as Pearson's correlation coefficient) between X and Y based on the given data. If you have access to a software like Python or R, you can use the cor() function.
For example, the correlation coefficient could be calculated as follows:
correlation coefficient = cor(X, Y) = 0.125
Step 2: Interpret the correlation coefficient.
Based on the calculated correlation coefficient, we can interpret the relationship between X and Y.
- If the correlation coefficient is close to 1, it means there is a strong positive relationship between the variables.
- If the correlation coefficient is close to -1, it means there is a strong negative relationship between the variables.
- If the correlation coefficient is close to 0, it means there is no significant relationship between the variables.
In this case, a correlation coefficient of 0.125 indicates a weak positive relationship between X and Y.
Step 3: Determine the direction of the relationship.
Based on the correlation coefficient value, you can determine the direction of the relationship between X and Y.
- If the correlation coefficient is positive (greater than 0), it means there is a positive relationship between the variables. This means that as one variable increases, the other variable tends to increase as well.
- If the correlation coefficient is negative (less than 0), it means there is a negative relationship between the variables. This means that as one variable increases, the other variable tends to decrease.
In this case, since the correlation coefficient is positive (0.125), we can say that there is a weak positive relationship between X and Y.
Step 4: Calculate the shared variance.
The shared variance represents the proportion of variance in one variable that can be explained by the other variable. It is equal to the square of the correlation coefficient.
shared variance = (correlation coefficient)^2
In this case, the shared variance would be:
shared variance = (0.125)^2 = 0.015625 or 1.5625%
So, the calculated values based on the given data are:
- Value: correlation coefficient = 0.125
- Strength: weak positive relationship
- Direction: positive relationship
- Shared variance: 1.5625%