Question

What is the purpose of using correlation as well as the interpretation of the correlation coefficient? In your video response, please describe at least 2 examples of an extremely low relationship among variables and an extremely high relationship among variables. Finally, discuss the two most common statistical techniques for determining relationships of variables.

Answer 1

Answer:

correlation

The term correlation is a measurement of how strong are two variables linearly related.

correlation coefficient:

Correlation coefficient is a number between -1 and 1 that shows the result of correlation. The closer it is to 1, the stronger positive linear relationship do the two variables have. The closer it is to -1, the stronger negative linear relationship do they have. If it's close to 0, weak linear relationship is indicated.

which represents correlation between x and y by term r which is correlation coefficient.

Examples:

1.Given a set of paired data (X,Y)

a. if Y is independent of X, then what value of a correlation coefficient would you expect?

b. if Y is linearly dependent on X, then what value of a correlation coefficient would you expect?

c. How could Y be closely dependent upon X yet r ≈ 0?

answer:: a. r = 0.

b. r ≈ 1 or r ≈ −1 (these two are same as |r| ≈ 1).

c. Y could be a quadratic function of X, as an example. The correlation coefficient is a measure of the scatter about a straight line—a linear function of X.

2.

A sample of size 50 produces a correlation coefficient r = 0.297. Test the hypotheses:     H0: ρ = 0.     HA: ρ > 0.     α = 0.05. df = 48, sr = 0.13782, t = 2.1549, P-value = 0.0181; since P-value < α, reject H0