1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.3. Graphical Techniques: Alphabetic
1.3.3.26. Scatter Plot

1.3.3.26.5.

Scatter Plot: Quadratic Relationship

Scatter Plot Showing Quadratic Relationship

Discussion

Note in the plot above how no imaginable simple straight line could ever adequately describe the relationship between X and Y--a curved (or curvilinear, or non-linear) function is needed. The simplest such curvilinear function is a quadratic model

\[ Y_{i} = A + BX_{i} + CX_{i}^{2} + E_{i} \]

for some A, B, and C. Many other curvilinear functions are possible, but the data analysis principle of parsimony suggests that we try fitting a quadratic function first.