GDB – Forum 8
Question 18.2

2. Describe the relationship between the two variables in the four plots. “Scatterplots are essential for understanding the relationships between variables. They provide a means for visual inspection of the data that a list of value for two variables cannot. Both the direction and the shape of a relationship are conveyed in a plot” (Cooper & Schindler). The x (horizontal axis) variable represents the variable that explains what we see in y (the vertical axis.) Often, x is a quantity which we can change or have control over. Or, to see how y reacts to different values of x. So x is usually called the independent or explanatory variable, and y the dependent or response variable. Another way to think about it, sometimes, is that x is used to predict y. So x is something that comes before y in time. Plot (a) seems do not have a correlation at all; there is no pattern to indicate where the data point lie. The points do not go in any particular direction; therefore this data has a correlation value of 0. No correlation occurs when there is no linear dependency between the variables. Plot (b) appears to have a positive correlation, although the data points are not very close together. Graph (b) would probably have a value of 0.3. A correlation is weaker the farther apart the points are located to one another on the line. Plot (c) You can see from the plot that these data don’t fit a straight line. There is a distinct bend near the left, and curve down to the right. When you have anything with a curve or bend, linear regression is wrong. This plot has a nonlinear relationship. Plot (d) While the points tend to be falling, it is a clearly negative relationship since points are not clustered as to show a clear straight line. It is a low negative correlation. Negative correlation occurs when an increase in one variable decreases the value of another. The line corresponding to the scatterplot is a decreasing line, this shows that as one variable increases, the other decreases.

Reference
Cooper, D.R., & Schindler, P.S. (2011). Business research methods (11th ed.). New York, NY; McGraw-Hill.