The figure below has six scatter diagrams for hypothetical data. The correlation coefficients are given alongside the figure.
While the solution is given, someone can "easily" identify them by first by checking if they are negative or positive. then, by how the dots are spread. Since I am thinking if there is a better way since I can't identify them without looking at the solution. Wonder if anyone can give a hand, how they would approach them in a more systematical way.
The correlation coefficient $r$ ranges from $-1$ through $1$. The absolute value $|r|$ roughly describes how well a (non-horizontal) line would do at describing the spread of data. So you can see how the plot with $r=-1$ precisely describes a line and $r=0.97$ would have very little error if you replaced all the data with a line. A line of best fit would do a worse and worse job of describing the data as $|r|$ drops all the way down to the example with $r=0.06$, which looks like totally randomized data.
The sign of $r$ describes whether the slope of that line of best fit would have a positive or negative slope. For instance, the $r=-1$ graph describes perfect negative correlation, where the independent variable varies inversely according to the dependent variable. A positive $r$, like the example where $r=0.97$, describes a positive correlation, where the two variables increase or decrease together.