Question

1. Discuss various ways of enhancing scatterplots
2. Discuss how coplots are constructed and provide the reasons for using such plots.
3. Discuss plots that can be used to check distributional assumptions.

Answer 1

Answers

a. Various ways of enhancing scaterplots:

answer:

1 ​​​​​​. Enhancing scatterplots with smothed densities

2. Enhancing scatterplots using Ellipsoid pixel placement and shading.

b.how coplots constructed and reason of using:

A conditional plot, also known as a coplot or subset plot, is a plot of two variables contional on the value of a third variable (called the conditioning variable). The conditioning variable may be either a variable that takes on only a few discrete values or a continuous variable that is divided into a limited number of subsets.

One limitation of the scatter plot matrix is that it cannot show interaction effects with another variable. This is the strength of the conditioning plot. It is also useful for displaying scatter plots for groups in the data. Although these groups can also be plotted on a single plot with different plot symbols, it can often be visually easier to distinguish the groups using the conditional plot.

Although the basic concept of the conditioning plot matrix is simple, there are numerous alternatives in the details of the plots.

1. It can be helpful to overlay some type of fitted curve on the scatter plot. Although a linear or quadratic fit can be used, the most common alternative is to overlay a lowess curve.
2. Due to the potentially large number of plots, it can be somewhat tricky to provide the axes labels in a way that is both informative and visually pleasing. One alternative that seems to work well is to provide axes labels on alternating rows and columns. That is, row one will have tic marks and axis labels on the left vertical axis for the first plot only while row two will have the tic marks and axis labels for the right vertical axis for the last plot in the row only. This alternating pattern continues for the remaining rows. A similar pattern is used for the columns and the horizontal axes labels. Note that this approach only works if the axes limits are fixed to common values for all of the plots.
3. Sanalysts prefer to connect the scatter plots. Others prefer to leave a little gap between each plot. Alternatively, each plot can have its own labeling with the plots not connected.
4. Although this plot type is most commonly used for scatter plots, the basic concept is both simple and powerful and extends easily to other plot formats.

c. Plots used to the distributional assumptions:

1 one commonly used metho is the probability plot (Gerson ,1975) of which the quantile-quantile (Q-Q) plot is a special case.

2.another graphical method is not as widely used as the probability plot is the

normal density plot (Jones and Daly, 1995; Hazelton 2003).