This document discusses correlation analysis and regression analysis. It begins by defining correlation as a measure of how two variables vary together. A positive correlation means the variables increase or decrease together, while a negative correlation means one variable increases as the other decreases. Regression analysis investigates the relationship between a dependent variable and one or more independent variables. An example is provided to illustrate calculating a correlation coefficient and testing hypotheses about relationships between variables using a regression model. Key terms discussed include the Pearson correlation coefficient, coefficient of determination, t-statistic, and developing a conceptual model for multiple regression analysis.

1. 1

2. Correlation and Regression Analysis
Lecture: 11
Dr. Muhammad Nawaz
2

3. Correlation Analysis
3

4. Correlation Analysis: Introduction
•Correlation is a measure of the degree to which two
variables vary together. In other words, two variables are
said to be correlated if they tend to simultaneously vary in
some direction.
•If both variables tend to increase (or decrease)
simultaneously, the correlation is said to be positive or
direct. If one variable increases and the other variables
decreases, the correlation is said to be negative or indirect.
•Management questions frequently revolve around the
study of relationships between two or more variables. Thus
a relational hypothesis is necessary.
•Various Objectives are served with correlation analysis.
•The strength, direction, nature of the relationship
(significance) and other features of the relationship may be
discovered.
•With correlation, one calculates an index to measure the
nature of the relationship between variables
4

5. Bivariate Correlation Analysis
(BCA)
• The Pearson (product moment) correlation
coefficient varies over a range of +1 through to
– 1.
• The designation r symbolizes the coefficient’s
estimate of linear association based on
sampling data.
• The coefficient p represents the population
correlation.
5

6. BCA contd.
• Correlation coefficient reveal the magnitude
and direction of relationships.
• The magnitude is the degree to which variables
move in unison or opposition.
• The size of a correlation of +.40 is the same as
one of -.40.
• The sign says nothing about size.
6

7. BCA contd.
• Direction tells us whether two variables
move in the same direction, opposite
direction.
• When variables move in the same
direction, the two variables have a positive
relationship:
– As one increases, the other also increases
– Family income, e.g., is positively related to
household food expenditure.
• As income increases, food expenditures increase.
7

8. BCA contd.
• Some variables move in the opposite
direction, e.g., the prices of products/
services and their demand. These
variables are inversely related.
• The absence of a relationship is
expressed by a coefficient of
approximately zero.
8

9. Scatterplots for Exploring
Relationships
• Scatterplot are essential for understanding
the relationships between variables.
• They provide a means for visual inspection of
data that a list of values for two variables
cannot.
• Both the direction and the shape of a
relationship are conveyed in a plot.
• The magnitude of the relationship can also be
seen.
9

10. Simple Bivariate (i.e., two-variable)
plot:
10

11. Correlation Matrix
• The correlation is one of the most common
and most useful statistics.
• A correlation is a single number that
describes the degree of relationship
between two variables.
11

12. Correlation Example
• Let's assume that we want to look at the relationship
between two variables, height (in inches) and self
esteem.
• Our hypothesis is that height affects one's self esteem.
• Data on the age and height of twenty individuals are
collected. We know that the average height differs for
males and females, so, to keep this example simple,
the example uses males only.
• Height is measured in inches. Self esteem is
measured based on the average of 10, 1-to-5, rating
items (where higher scores mean higher self
esteem). Here's the data for the 20 cases:
12

13. Calculating the Correlation:
13

14. Example contd.
• We use the symbol r to stand for the
correlation. The value of r will always be
between -1.0 and +1.0. if the correlation is
negative, we have a negative relationship; if it's
positive, the relationship is positive.
• N = 20
• ∑XY = 4937.6
• ∑X = 1308
• ∑Y = 75.1
• ∑X2 = 85912
• ∑Y2 = 285.45
14

15. Example contd.
• Plugging these values into the formula
given above, we get the value of r:
r = 0.73
• So, the correlation for our twenty cases
(.73) is shows a fairly strong positive
relationship.
• It seems that there is a relationship
between height and self esteem, at least in
this made up data!
15

16. Correlations
Compulsive
Buying F1 F2 F3 F4 F5 F6
Compulsive Buying Pearson Correlation 1 .873** .531** .117* .674** .469** -.110*
Sig. (2-tailed) .000 .000 .024 .000 .000 .034
N 371 371 371 371 371 371 371
F1 Pearson Correlation .873** 1 .317** -.105* .612** .262** -.140**
Sig. (2-tailed) .000 .000 .043 .000 .000 .007
N 371 371 371 371 371 371 371
F2 Pearson Correlation .531** .317** 1 -.095 .275** .105* -.061
Sig. (2-tailed) .000 .000 .069 .000 .044 .244
N 371 371 371 371 371 371 371
F3 Pearson Correlation .117* -.105* -.095 1 -.050 -.198** .105*
Sig. (2-tailed) .024 .043 .069 .341 .000 .043
N 371 371 371 371 371 371 371
F4 Pearson Correlation .674** .612** .275** -.050 1 .183** -.025
Sig. (2-tailed) .000 .000 .000 .341 .000 .626
N 371 371 371 371 371 371 371
F5 Pearson Correlation .469** .262** .105* -.198** .183** 1 -.070
Sig. (2-tailed) .000 .000 .044 .000 .000 .177
N 371 371 371 371 371 371 371
F6 Pearson Correlation -.110* -.140** -.061 .105* -.025 -.070 1
Sig. (2-tailed) .034 .007 .244 .043 .626 .177
N 371 371 371 371 371 371 371
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
16
Correlation:

17. Thanks to Allah
17

18. Regression Analysis
18

19. Regression analysis
• It investigates the dependence of one variable
known as dependent variable on one or more
variables known as Independent variable(s), and
providing an equation for estimating the average
value of DV from the known values of IVs.
• Regression analysis is a statistical method for
fitting an equation to a data set.
• It is used to estimate demand, production and cost
equations.
• A regression equation can be used for forecasting
purposes, i.e.,
– it predicts the value of the dependent variable for
given values of the independent variable.
19

20. Regression analysis contd.
• Estimation of the parameters of an equation
with more than one independent variable is
called multiple regressions.
• Estimated coefficients in a regression
equation measure the change in the value of
the dependent variable for each one-unit
change in the independent variable, holding
the other independent variables constant.
20

21. Regression analysis contd.
• The standard error of the estimate is the
measure of the error in prediction.
• The least-squares regression technique
can be used to quantify the relationship
between a dependent variable and one or
more independent variables.
21

22. Coefficient of Determination
R-square
• The coefficient of determination (R-
square) is used to test the explanatory
power of the entire regression equation.
• This statistic measures the proportion of
the total variation in the dependent
variable that is explained by variations in
the independent variables.
22

23. t-test
• t-statistic
• Hypotheses regarding the coefficients of
individual independent variables are tested
using t-statistic;
• t-statistic is computed by dividing the
estimated coefficient by its standard error;
23

24. Multiple Regression Analysis:
Example
• The first step in using multiple regression
analysis is to develop a conceptual model
based on economic theory.
• This model can specify the data that
should be collected and can also be used
to interpret results.
24

25. MRA Example
• Example: the following conceptual model is
based on cross-sectional data. The specification
of the model is given as:
Y = a + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + b6X6 (4.1)
Where,
– Y and X1-6 represent dependent and independent
variables respectively;
– b1-6 are the unknown parameters that are to be
estimated.
25

26. MRA Example contd.
• Variables are defined below:
• Y = Consumer Loyalty (CL)
• X1 = Self Image of the consumer (SI)
• X2 = Trust towards main service provider (Tr)
• X3 = Switching costs (SC)
• X4 = Customer service quality provided by
service provider (CSQ)
• X5 = Overall satisfaction from main cell service
provider (OS)
• X6 = Know how about mobile phones (KH)
26

27. MRA Example contd.
• The empirical model will take the following
form:
Y (CL) = a + b1SI + b2Tr + b3SC + b4CSQ + b5OS + b6KH
(4.2)
27

28. Hypotheses Testing
• The following six alternative hypotheses
(H1-6) are to be tested against six null (Ho)
hypotheses:
• H1: Self image of the consumer has a
positive effect on customer’s loyalty.
H1: b1 > 0
Ho: b1 = 0
28

29. Hypotheses Development contd.
• H2: Trust towards main service provider
has a positive effect on customer’s loyalty.
H2: b2 > 0
Ho: b2 = 0
• H3: Switching costs has a positive effect
on customer’s loyalty.
H1: b3 > 0
Ho: b3 = 0
29

30. Hypotheses Development contd.
• H4: Customer service quality provided by
service provider has a positive effect on
customer’s loyalty.
H1: b4 > 0
Ho: b4 = 0
30

31. Hypotheses Development contd.
• H5: Overall satisfaction from main cell
service provider has a positive effect on
customer’s loyalty.
H1: b5 > 0
Ho: b5 = 0
31

32. Hypotheses Development contd.
• H6: Knowledge about mobile phones has a
positive effect on customer’s loyalty.
H1: b6 > 0
Ho: b6 = 0
32

33. Regression Results Discussion
• In this analysis, a long run relationship has been
explored between
– customer loyalty of cell phone service provider
(dependent variable)
– with its construct, i.e.
• customer satisfaction,
• switching cost,
• self image of the mobile phone user,
• customer trust on services provider,
• over all service quality offered by cell services provider
and
• know how of customers (independent variables)
33

34. Regression Results Discussion
contd.
• Since there are many constraints prior to run
a multiple regression, the first thing that can
be examined prior to run a regression is to
check the fitness of the model , i.e.,
• How much of the variations in the dependent
variable is explained by the group of
independent variables.
34

35. Regression Results Discussion
contd.
• In Ordinary Least Square (OLS) method,
R-square is considered as a model fit.
• In the present analysis it is 65.5% (Table
1) which means, 65.5% variations in the
dependent variable are explained by the
set of independent variables, which is
good enough.
35

36. Table 1: Model Summary
R R-square
Adjusted
R-square
Std. Error of the
Estimate
.810 .655 .645 .7894
36

37. Results discussions contd.
• In Bivariate regression, t and F tests
produce the same results since t-square is
equal to F.
• In multiple regressions, the F test has an
overall role for the model, and each of the
independent variables is evaluated with a
separate t-test (Kothari 1990; Cooper and
Schindler 2003).
37

38. Table 2: ANOVA
Sum of
Squares
df Mean
Squar
e
F Sig.
Regression
Residual
Total
225.86
118.309
343.583
6
190
196
37.53
.62
60.228 .000
38

39. Results discussions contd.
• The analysis of variance and the ‘F’
statistic in Table 2 suggest that the model
is fit and it is valid with the existing set of
independent variables.
39

40. Results discussions contd.
• The coefficient estimates of the
independent variables are reported in
Table 3.
• The coefficient estimates, calculated
through OLS method, show that all of the
independent variables, except Know how,
have positive relationship with the
dependent variable, loyalty.
40

41. Table 3: Coefficients
Unstandard
Coefficients
B Std. Error
(1) (2)
Standard
Coefficients
Beta t Sig.
(3) (4) (5)
Constant .395 .321 1.230 .220
Self Image .127 .044 .152 2.861** .005
Trust .095 .064 .098 1.476 .141
Swit. Cost .099 .064 .076 1.558 .121
Service
Quality
.129 .079 .123 1.625* .106
Overall
Satisfact.
.520 .075 .522 6.940*** .000
Knowhow -.047 .040 -.054 -1.175 .241
41

42. Results discussions contd.
• Table 3 reports the coefficient estimates (b1—b6) of
the construct in column 2, and standard error of the
estimates in column 3. Column 4 reports the t- values
for each coefficient estimate and column 5 reports
the significance of the estimates at the specified
levels of significance.
• Self image of the cell phone user and over all
satisfaction from current service provider are the
statistically significant variables.
• Customer service quality provided by service
provider is significant but at a little higher than 10
percent level of significance.
42

43. • The t-values of switching cost to new service
provider, know how of cell services, and trust
towards main cell services provider are not
significant contributors towards customer
loyalty.
• It is only the self image of cell phone user and
the overall satisfaction from current cell service
provider which satisfy the customers; and
– it is obvious that only the satisfied customers
remain loyal to their service providers.
43

44. •The six alternative hypotheses, developed earlier,
have been tested against six null hypotheses, using
the t-values.
•The results of the test show that the coefficient
estimates of all the independent variables, except that
of the Know how about cell services, are positive
conveying the message that these five independent
variables have positive effect on customer loyalty.
•The coefficient estimate of know how is negative
(-.047).
•The important point to note here is that mere having
positive or negative signs for coefficient estimates are
neither necessary nor sufficient condition for making
a coefficient significant. 44

45. • It is the t-values of the estimates, at certain critical
level of significance, that make the corresponding
variable an important contributor. Looking at table
3 makes this point clear.
• The only two important contributors are self image
of cell users with t-value (2.86), and overall
satisfaction from current cell service provider with
t-value (6.94), both at a very high level of
significance.
• The case of customer service quality comes next
in significance with t-value (1.625) at low level of
significance (a little more than 10%).
45

46. Results discussions contd.
• The coefficient estimates of trust towards
main service provider, switching costs, and
know how (.095, .099, and -.047 respectively)
are not statistically different from zero as
shown by their t-values ( .1.478, 1.558, and -
1.175 respectively), hence the null
hypotheses (Ho: b2 = 0; Ho:b3 = 0, and
Ho:b3) can not be rejected, implying that they
have no effect on customer loyalty.
46

47. Conclusions
• Self image of the cell phone users and over
all satisfaction from current service provider
are the two significant contributors to
customer loyalty.
• The insignificance of the three independent
variables (trust, switching costs, and know
how) may have been the result of the
exclusion of some important variables -
purchase intent, repeat purchase behaviour,
perceived value – from the conceptual model.
47

48. Thanks to Allah
48

49. Theoretical framework
• Theoretical framework is developed
with the help of literature review.
49

50. Research Hypotheses
Research hypotheses are as follows:
H1: Age is has a relationship with compulsive buying.
H2: Tendency to spend is related to compulsive buying.
H3:Drives to spend compulsively is related to
compulsive buying.
H4: Feeling about shopping and spending is related to
compulsive buying.
H5: Dysfunctional spending is related to compulsive
buying.
H6: Post purchase guilt is related to compulsive buying.
50

51. Research Methodology
• Date Collection
Study was based on primary data. Data was
collected from college and university students from
Lahore, Islamabad and Bahawalpur of age 18 to 32
years.
• Sample Size & Technique
A total 371students completed the questionnaire.
There are 186 male and 185 female. Of the 400
respondents 371 (93%) have responded.
Convenience sampling method was used.
51

52. Research Methodology
• Instrument
Data was collected through structured
questionnaire. The compulsive buying scale
established by Edward (1993) was used to
measure compulsive buying behavior.
• Data Analysis Tool & Techniques
Techniques of Correlation and regression were
used.
52

53. Correlations
Compulsive
Buying F1 F2 F3 F4 F5 F6
Compulsive Buying Pearson Correlation 1 .873** .531** .117* .674** .469** -.110*
Sig. (2-tailed) .000 .000 .024 .000 .000 .034
N 371 371 371 371 371 371 371
F1 Pearson Correlation .873** 1 .317** -.105* .612** .262** -.140**
Sig. (2-tailed) .000 .000 .043 .000 .000 .007
N 371 371 371 371 371 371 371
F2 Pearson Correlation .531** .317** 1 -.095 .275** .105* -.061
Sig. (2-tailed) .000 .000 .069 .000 .044 .244
N 371 371 371 371 371 371 371
F3 Pearson Correlation .117* -.105* -.095 1 -.050 -.198** .105*
Sig. (2-tailed) .024 .043 .069 .341 .000 .043
N 371 371 371 371 371 371 371
F4 Pearson Correlation .674** .612** .275** -.050 1 .183** -.025
Sig. (2-tailed) .000 .000 .000 .341 .000 .626
N 371 371 371 371 371 371 371
F5 Pearson Correlation .469** .262** .105* -.198** .183** 1 -.070
Sig. (2-tailed) .000 .000 .044 .000 .000 .177
N 371 371 371 371 371 371 371
F6 Pearson Correlation -.110* -.140** -.061 .105* -.025 -.070 1
Sig. (2-tailed) .034 .007 .244 .043 .626 .177
N 371 371 371 371 371 371 371
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
53
Correlation:

54. Correlation Analysis
• The correlation analysis revealed the hierarchy of correlation.
Tendency to spend is highly correlated with correlation coefficient
of 0.873 and sig value of.000.
• The Second the most correlated variable is Dysfunctional
spending with correlation coefficient of 0.674 and sig value of .000.
• The third most correlated variable is Drives to spend compulsively
with correlation coefficient of 0.531 and sig value of .000.
• Fourth most correlated variable is Post purchase guilt with
correlation coefficient of 0.469and sig value of .000.
• The Fifth most correlated variable is Feeling about shopping and
spending with correlation coefficient of 0.117and sig value of
0.024.
• Finally the least correlated variable is Age with correlation value of
-.110 and sig value of 0.034
54

55. Regression Analysis (Table 2)
Unstandardized
Coefficients
B
t-Value Sig.
Age -0.292 -2.126 0.034
Tendency to spend 0.612 34.425 0.000
Drive to spend
compulsively
0.286 12.024 0.000
feeling about
shopping and
spending
0.063 2.262 0.024
Dysfunctional
spending
0.347 17.549 0.000
Post purchase guilt 0.242 10.213 0.000
55
Dependent Variable: Compulsive Buying

56. • The regression analysis in Table 2 yield a value of sig.
= 0.034 (Beta = -0.292, sig. = 0.034<0.05). We found
that compulsive buying and age are related and age
has a significant but negative relationship with
compulsive buying. Thus data support H1.
• The regression analysis in Table 2 yield a value of sig.
= 0.000 which is less than 0.01 (Beta = 0.612, sig. =
0.000<0.01). Thus compulsive buying behavior has
significant but positive relationship with tendency to
spend. Thus data support H2.
• The regression analysis of drive to spend compulsively,
and compulsive buying behavior in Table2 yield a value
of Beta = 0. 286, sig. = 0.000<0.01, shows a significant
but positive relationship. So H3 is accepted.
56
Data Analysis

57. • The regression analysis of feeling about shopping
and spending and compulsive buying in Table 2 yield
Beta = 0. 063, sig. = 0.024 shows a significant but
positive relationship. Hence H4 is accepted.
• The regression analysis of dysfunctional spending
and compulsive buying behavior in Table 2 yield a
Beta =0. 347, sig. = 0.000<0.01 shows significant but
positive relationship. Hence H5 is accepted.
• The regression analysis of post purchase guilt and
compulsive buying behavior in Table 2 Beta =0. 242,
sig. = 0.000<0.01 yield shows that significant but
positive relationship. Hence H6 is accepted.
57