In a recent study it was found that the correlation between

In a recent study it was found that the correlation between self-esteem and depression was -.64. Explain what this means. Calculate the coefficient of determination for this correlation and explain what information this provides.

Solution

(a) In a recent study it was found that the correlation between self-esteem and depression was -.64. Explain what this means.

r = correlation coefficient
* r measures the strength of the linear relationship between x and y
* values close to -1 or +1 indicate a strong linear relationship
* values close to 0 indicate a weak linear relationship
* the closer r gets to -1 or +1 the stronger the linear relationship is

Answer: Since r = -.64, it implies that there is a MODERATELY STRONG (since it is more than half way between 0 and -1), NEGATIVE (since r is negative) linear relationship between x = self-esteem score and y = depression score. This implies that the larger a person\'s self-esteem score is, the lower a person\'s depression score tends to be. (i.e. as x increases, y tends to decrease)

(b) Calculate the coefficient of determination

R^2 = coefficient of determination
R^2 = (r)^2
R^2 = (-.64)^2 = .4096 or 40.96%

Answer: .4096 or 40.96%

(c) and explain what information this provides.

R^2 = coefficient of determination
* R^2 measures the percent of variation in y that is explained by x
* 1-R^2 = the percent of variation that is attributed to chance variation and other factors

Answer: 40.96% of the variation in depression scores (y) can be explained by the self-esteem scores. This implies that 100% - 40.96% = 59.04% of the variation is attributed to chance variation and other factors.

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