Unit 1 BP801T Introduction to correlation

1. Introduction to Correlation
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 1

2. INTRODUCTION
Correlation quantifies the extent to which two
quantitative variables, X and Y, “go together.” When
high values of X are associated with high values of Y,
a positive correlation exists. When high values of X
are associated with low values of Y, a negative
correlation exists.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 2

3. Illustrative data set.
1. We use the data set bicycle.sav to illustrate
correlational methods.
2. In this cross-sectional data set, each observation
represents a neighborhood.
3. The X variable is socioeconomic status measured as the
percentage of children in a neighborhood receiving free or
reduced-fee lunches at school.
4. The Y variable is bicycle helmet use measured as the
percentage of bicycle riders in the neighborhood wearing
helmets.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 3

4. Twelve neighborhoods are considered:
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 4

5. 5. Three are twelve observations (n = 12). Overall, = 30.83
and = 30.883.
6. We want to explore the relation between socioeconomic
status and the use of bicycle helmets.
7. It should be noted that an outlier (84, 46.6) has been
removed from this data set so that we may quantify the linear
relation between X and Y.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 5

6. Scatter Plot
The first step is to create a scatter plot of the data.
“There is no excuse for failing to plot and look.”
1. In general, scatter plots may reveal a
• positive correlation (high values of X associated with high
values of Y)
• negative correlation (high values of X associated with low
values of Y)
• no correlation (values of X are not at all predictive of
values of Y).
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 6

7. These patterns are demonstrated in the figure to the right
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 7

8. Illustrative example.
2. A scatter plot of the illustrative data is shown to the
right.
3. The plot reveals that high values of X are associated with
low values of Y.
4. That is to say, as the number of children receiving
reduced-fee meals at school increases, bicycle helmet use
rates decrease’ a negative correlation exists.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 8

9. Illustrative example.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 9

10. 5. In addition, there is an aberrant observation (“outlier”)
in the upper-right quadrant.
6. Outliers should not be ignored—it is important to say
something about aberrant observations.
7. What should be said exactly depends on what can be learned
and what is known.
8.It is possible the lesson learned from the outlier is more
important than the main object of the study.
9. In the illustrative data, for instance, we have a low SES
school with an envious safety record. What gives?
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 10

11. CORRELATION COEFFICIENT
a. The General Idea Correlation coefficients (denoted r) are
statistics that quantify the relation between X and Y in
unit-free terms.
b. When all points of a scatter plot fall directly on a line
with an upward incline, r = +1; When all points fall
directly on a downward incline, r =- 1.
c. Such perfect correlation is seldom encountered. We still
need to measure correlational strength, –defined as the-
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 11

12. degree to which data point adhere to an imaginary trend
line passing through the “scatter cloud.”
d. Strong correlations are associated with scatter clouds
that adhere closely to the imaginary trend line.
e. Weak correlations are associated with scatter clouds that
adhere marginally to the trend line.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 12

13. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 13

14. f. The closer r is to +1, the stronger the positive correlation.
g. The closer r is to -1, the stronger the negative correlation.
Examples of strong and weak correlations are shown below.
Note: Correlational strength can not be quantified visually. It
is too subjective and is easily influenced by axis-scaling. The
eye is not a good judge of correlational strength.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 14

15. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 15

16. SIGNIFICANCE OF CORRELATION
The correlation coefficient, r, tells us about the strength
and direction of the linear relationship between X1 and X2.
The sample data are used to compute r, the correlation
coefficient for the sample.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 16

17. 1. The techniques which provide the decision maker a
systematic and powerful means of analysis to explore
policies for achieving predetermined goals are
called..........................
a. Correlation techniques
b. Mathematical techniques
C. Quantitative techniques
d. None of the above
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 17

18. 2. Correlation analysis is a ..............................
a. Univariate analysis
b. Bivariate analysis
c. Multivariate analysis
D. Both b and c
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 18

19. 3. If change in one variable results a corresponding change
in the other variable, then the variables
are.........................
A. Correlated
b. Not correlated
c. Any of the above
d. None of the above
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 19

20. 4. When the values of two variables move in the same
direction, correlation is said to be
............................
a. Linear
b. Non-linear
C. Positive
d. Negative
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 20

21. 5. When the values of two variables move in the opposite
directions, correlation is said to be
............................
a. Linear
b. Non-linear
c. Positive
D. Negative
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 21

22. 6. When the amount of change in one variable leads to a
constant ratio of change in the other variable, then
correlation is said to be .........................
A. Linear
b. Non-linear
c. Positive
d. Negative
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 22

23. 7. ...........................attempts to determine the
degree of relationship between variables.
a. Regression analysis
B. Correlation analysis
c. Inferential analysis
d. None of these
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 23

24. 8. Non-linear correlation is also
called.....................................
a. Non-curvy linear correlation
B. Curvy linear correlation
c. Zero correlation
d. None of these
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 24

25. 9. Scatter diagram is also called ......................
A. Dot chart
b. Correlation graph
c. Both a and b
d. None of these
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 25

26. 10. If all the points of a scatter diagram lie on a
Straight line falling from left upper corner to the right
bottom corner, the correlation is called...................
a. Zero correlation
b. High degree of positive correlation
C. Perfect negative correlation
d. Perfect positive correlation
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 26

27. 11. If all the dots of a scatter diagram lie on a straight
line falling from left bottom corner to the right upper
corner, the correlation is called..................
a. Zero correlation
b. High degree of positive correlation
c. Perfect negative correlation
D. Perfect positive correlation
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 27

28. 12. Numerical measure of correlation is called…………
A. Coefficient of correlation
b. Coefficient of determination
c. Coefficient of non-determination
d. Coefficient of regression
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 28

29. 13. Coefficient of correlation explains:
a. Concentration
B. Relation
c. Dispersion
d. Asymmetry
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 29

30. 14. Coefficient of correlation lies between:
a. 0 and +1
b. 0 and –1
C. –1 and +1
d. – 3 and +3
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 30

31. 15. A high degree of +ve correlation between availability
of rainfall and weight of people is:
a. A meaningless correlation
b. A spurious correlation
c. A nonsense correlation
D. All of the above
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 31

32. 16. If the ratio of change in one variable is equal to the
ratio of change in the other variable, then the correlation
is said to be ......
A. Linear
b. Non-linear
c. Curvilinear
d. None of these
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 32

33. 17. If r= +1, the correlation is said to be…….
a. High degree of +ve correlation
b. High degree of –ve correlation
C. Perfect +ve correlation
d. Perfect –ve correlation
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 33

34. 18. If all the points of a dot chart lie on a straight line
vertical to the X-axis, then coefficient of correlation is
.........
A. 0
b. +1
c. –1
d. None of these
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 34

35. 19. If all the points of a dot chart lie on a straight line
parallel to the X-axis, it denotes ................of
correlation.
a. High degree
b. Low degree
c. Moderate degree
D. Absence
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 35

36. 20. The unit of Coefficient of correlation is ..
a. Percentage
b. Ratio
c. Same unit of the data
D. No unit
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 36

37. 21. The –ve sign of correlation coefficient between X and Y
indicates.............................
a. X decreasing, Y increasing
b. X increasing, Y decreasing
C. Any of the above
d. There is no change in X and Y
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 37

38. 22. Coefficient of correlation explains .........of the
relationship between two variables.
a. Degree
b. Direction
C. Both of the above
d. None of the above
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 38

39. 23. For perfect correlation, the coefficient of correlation
should be ..........................
A. ± 1
b. + 1
c. – 1
d. 0
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 39