The correlation coefficient can take values from -1 to 1. If the correlation coefficient lies in the range (-1,0) then we say that the correlation is negative, on the other hand if the correlation coefficient lies between (0,1) then the correlation is said to be positive.
a) What the correlation means in words. (For example, in a positive correlation we could say "As ____ increases, _____ increases.")
If on increase of one variable, another variable also increases, then we say that there is positive correlation between those two variables, on the other hand if increasing one variable results in decrease in second variable, then we say that the negative correlation exists.
b) The general interpretation of the correlation coefficient, i.e., whether it is a very strong relationship, a moderate relationship, a weak relationship, etc.
If the correlation coefficient is near 1 or -1 then we say that there is strong positive or negative correlation respectively.
If the correlation coefficient is between 0.4 to 0.7 then we say that it is moderate relationship.
If the correlation coefficient is less than 0.4, then we say that the correlation is weak.
c) The correlation between grades in basic math and advanced math classes at a small liberal arts college where r = +.78.
Here we are given that the correlation is r = + 0.78, means there is high positive correlation between the considered variables.
d) The correlation between reading ability and social science grades in a middle school where r = +.52.
Here we are given that the correlation is r = + 0.52, means there is there is moderate relationship between the considered variables.
e) The correlation between test anxiety scores and grade on an achievement test where r = -.42.
There is negative correlation between test anxiety scores and grade on an achievement test.
f) The correlation between math aptitude scores and musical aptitude scores in second graders where r = +.28.
There is weak positive correlation between the between math aptitude scores and musical aptitude scores in second graders.
g) The correlation between the number of books read over a year and the scores on a popular video game where r = -.38.
There is weak negative correlation between the number of books read over a year and the scores on a popular video game.