The linear correlation coefficient "r" gives you an idea of the relationship between two variables. The correlation coefficient has an absolute value between 0 and 1, where a coefficient with a value equal to zero, indicates that there is no linear correlation between the variables and a coefficient with an absolute value equal to 1 indicates that there is a strong linear correlation between the variables.
If the correlation coefficient is negative, then the relationship between the variables is inverse, which means that as one of the variables increases, the other variable decreases. Graphically, large values of one of the variables corresponds to small values of the other variable, and to small values of one variable correspond high values of the other variable:
If the correlation between two variables is positive, it means that the relationship between both variables is direct, so as one variable increases, the other variable also increases. Graphically, to a large value of one variable corresponds to large values of the other variable, and to small values of one variable correspond to small values of the other variable:
When there is no correlation between the variables, r=0, the values of the variable form a "cloud" on the dot plot, this indicates that large values of one of the variables can correspond to large or small values of the other variable and the same happens to small values of the variable:
1. The data set that appears to have a correlation equal to 1 is the dot plot, where the points align to form a line with a positive slope.
The graph that shows a correlation with r=1 is Figure 4.
2. The data set that appears to have a correlation coefficient close to -1 will be the one where the points seem to form a line with a negative slope.
The graph that shows a correlation with an approximate correlation coefficient of -1 is Figure 3.
3. The data set that shows two variables with no correlation is the dot plot where the dots do not line up in any way, the data on the graph looks like a cloud. The graph that shows two variables that have no correlation is Figure 2.