what is the most likely answer for the confidence coefficient of linear correlation if x = the number of hours spent studying for a test, and y = the number of points earned on the test?
Since this is not my area of expertise, I searched Google under the key words "correlation 'confidence coefficient'" to get this:
http://en.wikipedia.org/wiki/Confidence_interval
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
To find the confidence coefficient of linear correlation, we need to calculate the correlation coefficient, also known as "r". The correlation coefficient measures the strength and direction of the linear relationship between two variables.
To calculate "r", follow these steps:
Step 1: Collect data by recording the number of hours spent studying (variable x) and the number of points earned on the test (variable y) for a sample of individuals.
Step 2: Calculate the mean (average) of x and y, denoted as x̄ and ȳ, respectively.
Step 3: Calculate the difference between each x value and x̄, and the difference between each y value and ȳ.
Step 4: Multiply each pair of differences obtained in Step 3. Sum all of these products.
Step 5: Calculate the square root of the sum of squares of differences of x (Step 3) and the sum of squares of differences of y (also Step 3), denoted as √(Σ(x - x̄)²) and √(Σ(y - ȳ)²) respectively.
Step 6: Divide the sum obtained in Step 4 by the product of the square roots obtained in Step 5.
Step 7: The result of the division in Step 6 is the correlation coefficient "r". It will fall between -1 and 1, where -1 indicates a strong negative linear relationship, 1 indicates a strong positive linear relationship, and 0 indicates no linear relationship.
The confidence coefficient is not directly calculated. However, by using the correlation coefficient "r", you can calculate the confidence interval around it to estimate the true correlation value in the population.