1 1. Explore the model and note what it tells you about this particular set of data

SOLUTION:
Consider the 3-D scatter plot. Here it is a multivariate data of the form
(x,y,z) where x stands for MPG, y for weight and z for acceleration. The
sample consists of observations which come from 3 different populations
hence form 3 different clusters. The populations are European, Japanese
and Americans and they are represented by 3 colours- red, ash and
purple. The 3-D scatter plot helps us to understand the linear
correlations between these variables (either only these variables or for a
fixed value of a 4th variable) amongst each cluster and then as a whole.
In my explanation I will assume the linear model i.e. I will try to explain
the fit of the following linear model to this data.
Z = a x + b y +ε where ε~(0,1)
All correlations mentioned so-forth will be linear correlations. Since the
3-D plot is difficult to view in a 2-D page, the projections of the scatter
plot has been taken on the x-z axis and the y-z axis.
First I will discuss about the projection of the scatter plot on the x-z
axis. Hence we study the 2-D scatter plot between MPG and
acceleration. First note the plot as a whole ignoring the clusters that
have been formed by the 3 populations. It can be clearly seen that MPG
and Acceleration have positive linear correlation. In general we can say
(if we ignore the colours) that acceleration will be higher for bigger
values of MPG. But the result is actually not true for the whole
population. The explanation is that while deducing these...