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1. Theoritical Statistics
Example 1:
(a) Find the correlation between these two variables.
r = -0.2013
(b) Relationship between these two variables is weak. Does your calculation of the correlation support this
statement? Explain your answer.
The interesting part is that the relationship seems to be negative, most likely caused by the extra ordinary student. Lets
remove that point and recalculate r. Without the outlier the r value is now 0.3222, which says that the association while
very weak it is positive. Should we eliminate that student? How likely is it that a person can get the worst score on the
first and then score the highest on the final? What are we interested in displaying the possible outcomes on the majority
of the group or all of the group. You can again see that r is not resistant to outliers thus, we should be careful when
outliers appear, and decide whether we need to eliminate them to get a better understanding of the entire group and not
just the unusual point.
(a) Find the correlation between these two variables.
r = 0.5194
(b) The relationship between these two variables is stronger than the relationship between the two variables in
the previous exercise. How do the values of the correlations that you calculated support this statement? Explain
your answer.
First Final
153 145
144 140
162 145
149 170
127 145
118 175
158 170
153 160
Relationship Between First Exam and Final Exam
110
120
130
140
150
160
170
180
110.00 120.00 130.00 140.00 150.00 160.00 170.00
First Exam Score
FinalExamScore
125
135
145
155
165
175
125 135 145 155 165
First Exam Score
FinalexamScore

2. The variation about a straight line seems to be less and as the second exam score increases there is a larger increase in
the average value of the final exam score. Yet one can still see a quite a lot of variation about the average trend line, thus
the reason for the correlation value of 0.5194.
130
140
150
160
170
180
190
200
130 140 150 160 170 180
Score for Second Exam
ScoreonFinal
Example 2:
Refer to the previous exercise. Add a ninth student whose scores on the second test and final exam would lead
you to classify the additional data point as an outlier. Recalculate the correlation with this additional case and
summarize the effect it has on the value of the correlation.
Second Final
1 158 145
2 162 140
3 144 145
4 162 170
5 136 145
6 158 175
7 175 170
8 153 160
9 200 200
The ninth student gets two perfect scores on the second and the final (assuming that 200 is the most one can
score). The corresponding r value is 0.8015. This is quite a large change from r = 0.5194.

3. 130
140
150
160
170
180
190
200
130 140 150 160 170 180 190 200 210
Score for Second Exam
ScoreonFinal
Example 3:
Make a scatterplot find the correlation r. Explain why r is close to zero despite a strong relationship between
speed and gas used.
The value of r = -0.1716
The value of r only measures how close our data
follows a linear relationship, which this situation
does not.
Notice r = 0 despite the fact that we do not have a
straight line. This shows the importance of looking
at the scatterplot.
Example 4:-
What's wrong? Each of the following statements
contains a blunder. Explain in each case what is wrong.
(a) "There is a high correlation between the gender of American workers and their income."
Gender is a categorical variable. The correlation value r is only to be used to indicate linear association between two
quantitative variables.
(b) "We found a high correlation (r = 1.09) between students' ratings of faculty teaching and ratings made by other
faculty members."
The r value can only be a number in the interval [-1, 1].
Chart Title
0
5
10
15
20
25
0 50 100 150 200
Speed (km/h)
FuelSpent(l/100km)
Fuel
Linear (Fuel)

4. (c) "The correlation between planting rate and yield of corn was found to be r = 0.23 bushel."
The statistic r is a unitless number, thus the statement above, “…was found to be r = 0.23 bushel." attaches a unit to r
which is not correct. The correlation r does not depend on the unit of the measurement.