Extra exercise 20
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1. Our intuition for the line is better when there is a clear
pattern. One situation where our intuition may fail us is when
one or several points fall clearly outside the pattern of the 
other points. How to weight the fit of the outlying points with
the fit of those that form a linear relation is difficult to 
get a sense of without using some formula (which the least squares
equation does, of course).

2. When the points at the most extreme x-values are moved,
the impact on the fitted line is stronger. Moving around the third
point along the x-axis does not affect the line much. If we also
change the positions of the points on the x-axis from being equidistant
(the default) to forming a group of four with one point far from the
group, the impacts become very different when moving points within the
group and the single point outside the group. For a line with intercept
close to 0 and slope equal to 1, it is probably easiest to start with
relatively few points (3 is the lowest number), move those roughly to
match the line and then add extra points.

3. Maybe a linear pattern starts to become visible at values of +-0.3.
Clear patterns need values correspond to values +-0.5.

4. The correlation coefficient is definitely not robust. The spread of
points along the x-axis affects the strength of the correlation. With
all the points along the x-axis close together, correlations tend to be
low, and moving them apart will increase the correlation.

5. With points exactly horizontal, the applet will not show a
correlation of zero. With points exactly on the line close to 
horizontal, the correlation will be +1 if the slope is positive 
and -1 if the slope is negative. A similar behaviour is seen
with points on a vertical line. If the line is exactly vertical, no
correlation is shown, but slopes of +1 and -1 will appear when the 
points match a line close to vertical.