**Scatterplot Matrix
of family Food Expenditure, Income and Size
Motivation:** Oftentimes, it may not be realistic to
conclude that only one factor or IV influences the behavior of the DV. In such
situations, a researcher needs to carefully identify those possible factors and explicitly
include them in the Linear Regression Model (LRM). Both the existing theory and common
sense should constitute a basis for selecting the IVs; and where data on a theoretical
variable is not readily available a proxy should be chosen carefully. Graphical
assessment of both the type and the structure of correlation among the variables can be
accomplished by using the scatterplot matrix - a graphical device that consists of
scatterplots for each pair of variables in the model.

**Problem Description and Data
**The maintained hypothesis is essentially similar to the

The additional data on family size is as follows (Source: Hamburg et al., 1994, p. 507):

X

3 |
3 |
2 |
1 |
4 |
2 |
3 |
2 |
1 |
6 |
3 |
4 |
1 |
5 |
3 |
1 |
6 |
5 |
2 |
2 |

**The Scatterplot matrix is an important graphical tool for
screening the data to visually identify the following possibilities:**

1. **Type of relationship** between the variables (a pair at a time) - **Direct
or Indirect**

2. **Form of relationship** between the DV and the IV_{s} - **Linear
or Nonlinear**

3. **Degree of relationship** between any two variables - from **Perfectly
Strong and Direct** **(r = +1)** to **Perfectly Strong and
indirect (r = -1)**. **No relationship** at all if **r = 0**

4. Presence/Detection of **Outliers** in the data set.

**The above matrix suggests the following conclusions: **

1. The relationship between annual family **Food Expenditure** and **Size**
is **Direct, Linear,** and relatively **Strong** with possibly
one **OUTLIER**.

2. The relationship between annual family **Food Expenditure** an I**ncome**
is **Direct, Linear**, and relatively **Strong** with no
apparent **OUTLIER**.

3. The relationship between family **Size** and annual **Income**
is **Direct, Linear**, and **Weak** with one visible **OUTLIER**.
Thus we should expect **collinearity** problem in the regression.

Quantitative assessment of both the type and the structure of correlation among the
variables is the subject matter discussed under the multiple regression and correlation analysis.

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**Copyright© 1996, Ebenge Usip, all rights reserved.
Last revised: Wednesday, July 10, 2013.**