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IOSR Journal of Business and Management (IOSR-JBM)
e-ISSN: 2278-487X, p-ISSN: 2319-7668. Volume 23, Issue 4. Ser. II (April 2021), PP 23-34
www.iosrjournals.org
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 23 | Page
Developing a Research Methodology with the Application of
Explorative Factor Analysis and Regression
Dr Priyabrata Panda1, Sovan Mishra2, Dr Bhagabat Behera3
Abstract
Developing a methodology for an article or thesis has immense importance. Jharotia & Singh (2015) said that
methodology eases the work plan of a thesis. Patel & Patel (2019) added that research methodology is the mean
to resolve research issues scientifically. The principal purpose of this research work is to develop a methodology
when factors are generated after applying explorative factor analysis and regression is to be applied to such
factors. This current work also enlightened data screening process and normality assumption. It will help the
researchers who are conducting perception studies, behavioural studies etc. with categorical data.
Keywords: Explorative Factor Analysis, Regression, Methodology, Data Screening, Normality
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Date of Submission: 22-03-2021 Date of Acceptance: 06-04-2021
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I. Introduction
The methodology segment of a thesis or article has immense importance as it helps to proceed for further
analysis. Jharotia & Singh (2015) emphasised that methodology defines work plan for completion of research.
Patel & Patel (2019) added that research methodology is the way to solve research problem scientifically. This
part of a research work includes a series of activities in sequence like formulation of statement of the problem,
comprehensive design of a research which includes its scope, required data, sampling design etc. Crafting a
research methodology chapter largely depends on the type and nature of research. This chapter for time series data
is different from panel data. This work is specifically designed for a research work which applied linear regression
after generating factors from explorative factor analysis with the help of principal component analysis. The
research methodology chapter of an ongoing Ph D thesis of Mishra (2021) has been taken as a background for
this research work.
II. Objective of the Study
The main purpose of the study is to develop a methodology of a research work which applies regression
on factors extracted from principal component analysis under explorative factor analysis. Data screening and
assumption testing are also highlighted.
III. Research Design
Research design answers what, why, where and how (Kothari, 2004). It narrates about the data, type of research,
variables, sample etc. which are enumerated below.
Type of Research
Empirical research differs from exploratory research. Researcher has to mention about the type of research here.
Nature of Data
Primary data and or secondary data are applied for hypothesis testing. Moreover, objective of a research specifies
the type of data which are to be used. The researcher should theoretically justify the requirement of data in
accordance with objectives.
Source of Data
The sources of data must be reliable. Government sources are said to be authentic. CMIE database is widely used
by different researchers. Primary data must be collected from targeted population with comprehensive scheduled
questionnaire.
1 Assistant Professor of Commerce, Gangadhar Meher University, Amruta Vihar, Sambalpur, Odisha,
India, 7978123683, pandapriyabrata@rocketmail.com
2 Research Scholar, Ravenshaw University, Cuttack, India
3 Assistant Professor of Commerce, Ravenshaw University, Cuttack, India
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 24 | Page
Questionnaire and Scale Development
Development of questionnaire depends on objectives. Past literatures must be referred in this regard. The
first part must include the demographic information of the respondents. Five-point scale or seven-point scale is
desired. Scale development facilitates reliability and validity measures (Tay & Jebb, 2017). Research work of
Churchill & Peter (1984), Morgado (2017), Carpenter (2018), Worthington & Whittaker (2006) may be referred
for scale development.
Variables
Name of variables and their justification must be mentioned. Dependent variables, independent variables and
control variables should be specifically described. Proper citation of earlier literatures must be made.
Sampling Design and Selection of Sample Unit
Probability method of sampling is preferred for collection of primary data. Purpose of the study, population size,
sampling error etc. determine the size of sample (Israel, 1992). Selection of sample units from a population has
immense importance. The proper determination of sample units reduces standard error and confirms robust
inferences. Yamane (1967) formula is quite popular for determining sample size with finite population. Krejcie
& Morgan (1970) table has been used by many researchers for sample size determination in “known populations”.
Other literatures like Jones et. al., (2003), Taherdoost (2017), Blessing & Oribhabor & Anyanwu (2019) have
contributed a lot to the sample size determination theory. Sample size also depends on the concerned statistical
tool which is being applied in the research work. Like, Kline (1998) infered that sample size may be 10 to 20
times of variables when structural equation modelling is applied. In addition, KMO test confirms sample adequacy
when explorative factor analysis is applied.
Scope of the Study
Scope of the study includes geographical scope, parameter scope, time scope etc. The limit and range of the study
need to be particularly mentioned.
IV. Data Cleaning
Data cleaning process ensures a comprehensive data set with zero error. It digs out any missing values and outliers.
The careless response or unengaged responses are also traced out and ignored before deciding the final data set.
Missing Data
Table 1: Missing Data of Demographic Variables
Valid/Missing
Gender
Age
Income Level
Occupation
Valid
217
217
217
217
Missing
0
0
0
0
Source: Authors own Compilation
It is found in the table that there are no missing values for all the four variables in the above table. Two hundred
seventeen responses are observed with no missing values.
Unengaged Responses
There may be possibilities of some careless responses. It may happen that a respondent may select same option
for all variables. It will lead to fallacious derivations. Thus, an attempt is made to omit such responses.
Table 2: Unengaged Responses
Responses Standard Deviation
1. 0.418854
2. 0.455414
3. 0.455562
4. 0.461251
5.
0.466324
Source: Authors own Compilation
Row wise standard deviation is calculated to find such responses. If the value of standard deviation tends
to be zero, it means a respondent have selected same option carelessly for all the variables. The above table shows
row wise standard deviation of some responses in ascending order which is not zero. Thus, it is inferred that there
are no unengaged responses in the data set.
Outliers
Outliers are the extreme values of a data series or data set. If the standardised value exceeds +-3, the data point is
said to be an outlier. In the table below, there are no outliers as the standardised value of all the variables are
within +-3.
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 25 | Page
Table 3: Standardised Value and Outliers
Standardised Variables N Minimum Maximum Desired Value
Z score: X1 22 -1.02203 2.70875
+3 to -3
Z score: X2 22 -.51835 2.22934
Z score: X3 22 -2.22089 2.12708
Z score: X4 22 -2.47221 .41740
Z score: X5 22 -.43054 2.44132
Source: Authors own Compilation
V. Reliability Analysis
The table below measures reliability statistics of pilot study with the help of Cronbach’s alpha (1951). Further,
Churchill & Peter (1984) inferred that reliability is necessary for valid research. Such value must be more than .7
(Nunnally, 1978; Nunnally, 1988).
Table 4: Reliability Statistics of Pilot Study
Cronbach's Alpha
No of Items
.775
19
Source: Authors own Compilation
The table above reveals the Cronbach’s alpha value .776 for 78 respondents. The value satisfies the recommended
criteria.
Table 5: Reliability Statistics of Total Sample
Cronbach's Alpha
No of Items
.786 19
Source: Authors own Compilation
The table shows the reliability statistics through Cronbach's Alpha value for the full sample which consists of 217
responses. Such value is .786 which also satisfies the recommended criterion.
VI. Factor Analysis
Factor analysis may be categorised into following categories.
1. Exploratory factor analysis.
2. Confirmatory factor analysis.
3. Structural equation modelling.
Exploratory factor analysis is analysed in the present study with the help of SPSS software4.
Kaiser Meyer Olkin (KMO) test of Sampling Adequacy and Bartlett's Test of Sphericity
Table 6: KMO and Bartlett's Test Result
Kaiser
-
Meyer
-
Olkin Measure of Sampling Adequacy
.749
Bartlett's Test of Sphericity
Approx. Chi
-
Square
643.795
df
171
Sig.
.000
Source: Authors own Compilation
The table above portrays Kaiser-Meyer-Olkin (KMO) and Bartlett statistics. Kaiser-Meyer-Olkin’s value
measures the adequacy of sampling (Ayuni & Sari, 2018; Hadi, et. al., 2016). KMO statistics is calculated with
the following formula (Kaiser, 1970).
Where r is simple correlation and u is the partial correlation between i and j.
4 https://stats.idre.ucla.edu/spss/seminars/introduction-to-factor-analysis/a-practical-introduction-to-
factor-analysis/
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 26 | Page
Such value ranges from 0 to 1. A value near to one and farer to zero infers that a sample is adequate for
factor analysis. To be particular, such value should be more than .5 (Kaiser, 1970; Field, 2000) and .6 (Pallant,
2013, Shree et al., (2017). Hutcheson & Sofroniou (1999) opined that “KMO value from .7 to .8 is good, .8 to .9
is great and above .9 is superb”. In this research work, KMO value is .749 which is good and within the
recommended value according to above all criteria.
On the other hand, Bartlett's Test of Sphericity (Bartlett, 1950,1951) measures the relatedness of
variables. The null hypothesis for such test is that variables are uncorrelated. Correlation among some of the
variables are required to apply factor analysis. Further, a population matrix is having 1 in diagonal and 0 in non -
diagonal, a sample drawn from the population cannot be fit for factor analysis (Tobias & Carlson, 2010). Thus,
the null hypothesis must be rejected at least at 5% level of significance (Shree et. al., 2017). Such test is also
recommended by Knapp and Swoyer (1967); Gorsuch, (1973). The null hypothesis here is rejected at 1% level of
significance as the p value is 0.00 as shown in the above table. It can be inferred that variables are correlated and
can be processed for factor analysis.
Factor Extraction
Factor extraction can be carried on by many methods like Scree test (Catell, 1996), Parallel Analysis
(Horn, 1965), Principal Component Analysis (PCA) (Pallant, 2013). PCA is widely used. It gives better results
(Sehgal et.al., 2014). Mishra et. al., (2017) mentioned that PCA can extract and group inter-correlated variables
from a statistical data. Thus, PCA method is applied here.
Communalities
Communalities are the variance or squared factor loadings of variables. It explains the proportion of
variability which is explained by the factors and its value is same in spite of using unrotated factor loadings or
rotated factor loadings5. Its value ranges from 0 to 1. The value closer to one infers that such variable is well
explained by the factors. Communalities value decides retaining or removing a variable. But there is a debate in
deciding the accepted value of communalities. Osborne (2014) opined that communalities more than 0.4 can be
accepted whereas Child (2006) inferred that a variable can be removed if its communality value is less than 0.2.
In the present study, variables with communality value nearer 0.5 or more are retained for further analysis.
Table 7: Communalities
SL No Variables Initial Extraction
1.
X1
1.000 .656
2.
X2
1.000 .702
3.
X3
1.000 .643
4.
X4
1.000 .547
5.
X5
1.000 .557
6.
X6
1.000 .286
7.
X7
1.000 .689
8.
X8
1.000 .451
9.
X9
1.000 .585
10.
X10
1.000 .476
11.
X11
1.000 .468
12.
X12
1.000 .484
13.
X13
1.000 .478
14.
X14
1.000 .594
15.
X15
1.000 .493
16.
X16
1.000 .636
17.
X17
1.000 .418
18.
X18
1.000 .635
19.
X19
1.000 .469
Source: Authors own Compilation
5 https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/multivariate/how-
to/factor-analysis/interpret-the-results/all-statistics-and-graphs/.
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 27 | Page
In the table above, such value for all the variables is more than .4 except X6 which is removed and PCA is again
undertaken. The results are shown below.
Table 8: Communalities After Deleting One Variable
SL No Variables Initial Extraction
1.
X1
1.000 .670
2.
X2
1.000 .701
3.
X3
1.000 .640
4.
X4
1.000 .587
5.
X5 1.000 .555
6.
X6
1.000 .657
7.
X7
1.000 .443
8.
X8
1.000 .576
9.
X9
1.000 .487
10.
X10
1.000 .476
11.
X11
1.000 .488
12.
X12 1.000 .489
13.
X13 1.000 .593
14.
X14 1.000 .530
15.
X15 1.000 .700
16.
X16 1.000 .413
17.
X17 1.000 .628
18.
X18
1.000 .470
Source: Authors own Compilation
The variable X16 is having communality .413 which is dropped and EFA is undertaken again. The communality
value, Kaiser-Meyer-Olkin Measure of Sampling Adequacy and Bartlett's Test of Sphericity is shown below after
dropping such variable.
Table 9: KMO and Bartlett's Test
Kaiser
-
Meyer
-
Olkin Measure of Sampling Adequacy.
.720
Bartlett's Test of Sphericity
Approx. Chi
-
Square
551.584
df
136
Sig.
.000
Source: Authors own Compilation
The KMO and Bartlett's Test statistics are matching with the recommended criterion as mentioned above.
Table 10: Communalities of Selected Variables
SL No Variables Initial Extraction
1.
X1
1.000 .676
2.
X2
1.000 .696
3.
X3
1.000 .630
4.
X4
1.000 .580
5.
X5
1.000 .550
6.
X6
1.000 .660
7.
X7
1.000 .486
8.
X8
1.000 .599
9.
X9
1.000 .488
10.
X10
1.000 .478
11.
X11
1.000 .491
12.
X12 1.000 .484
13.
X13 1.000 .616
14.
X14 1.000 .543
15.
X15 1.000 .718
16. X16 1.000 .626
17.
X17 1.000 .498
Source: Authors own Compilation
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 28 | Page
The communalities of all the variables in the above table is nearer or more than .5. A total of seventeen
variables are processed for further analysis.
In the table below, the total column portrays the eigen value which explains the amount of variance of a
factor or component for original variables. Such variance is termed in percentage in the next column followed by
the cumulative percentages. A value more than 1 can be accepted for selecting number of components. In this
research work, six components are selected for further analysis where eigen value is more than 1. The extracted
variance explained for these six factors is 57.64% which more than the recommended value i.e.,50%. Thus, all
the seventeen variables explain 57.64% of the total information.
Table 11: Total Variance Explained
Factor
Initial Eigenvalues
Extraction Sums of Squared Loadings
Rotation Sums of Squared Loadings
Total
% of Variance
Cumulative %
Total
% of Variance
Cumulative %
Total
% of Variance
Cumulative %
1
3.37
19.84
19.84
3.37
19.84
19.84
1.87
11.01
11.19
2
1.75
10.33
30.17
1.75
10.33
30.17
1.78
10.50
21.52
3
1.28
7.57
37.75
1.28
7.57
37.75
1.58
9.32
30.84
4
1.20
7.10
44.86
1.20
7.10
44.86
1.57
9.27
40.24
5
1.12
6.60
51.46
1.12
6.60
51.46
1.50
8.83
48.96
6
1.05
6.17
57.64
1.05
6.17
57.64
1.47
8.68
57.64
7
.973
5.72
63.36
8
.882
5.18
68.55
9
.748
4.39
72.94
10
.738
4.34
77.29
11
.675
3.96
81.25
12
.644
3.787
85.045
13
.603
3.544
88.589
14
.570
3.352
91.942
15
.512
3.012
94.954
16
.461
2.713
97.667
17
.397
2.333
100.000
Extraction Method: Principal Component Analysis.
Source: Authors own Compilation
Rotated component matrix, in the table below, explains the factor loadings which is the correlation
between the variable and the factor or component. Four factors are grouped under factor 1. Three variables are
grouped under factor 2. Third factor includes two variables. Fourth factor includes three variables. Fifth factor
includes three variables viz. X13, X14 and X15. X16 and X17 are grouped under the sixth component or factor.
Researchers often faced issues while naming such factors or components. With rigorous literature review and
theoretical background, factors may be given required names. After generating factors from rotated component
matrix, reliability of all variables is again calculated.
Table 12: Rotated Component Matrix
Variables
Component
Factors
1
2
3
4
5
6
X1
.745
Factor 1
X2
.610
X3
.587 .471
X4
.475 .313
X5
.786
Factor 2
X6
.604
X7
.572 .331
X8
.798
Factor 3
X9
.713
X10
.827 Factor 4
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 29 | Page
X11
.642
X12
.346 .423 .367
X13
.747
Factor 5
X14
.353 .486
X15
-.327 .318 .377
X16
.800
Factor 6
X17
.698
Source: Authors own Compilation
Table 13: Reliability Statistics of Extracted Factors.
Cronbach's Alpha
N of Items
.740 17
Source: Authors own Compilation
The reliability statistics with the help of Cronbach’s Alpha of all variables is .740 which is also more than the
recommended level.
VII. Test of Normality
Normally distributed data yields robust inferences. Thus, examining such assumption is essential before
proceeding to further analysis to avoid inconsistent result (Das & Imon, 2016, Ghasemi & Zahediasl, 2012, Kwak
& Park, 2019). Many statistical tests need satisfaction of normality assumption. (Mishra et. al., 2019). Thus,
normality of all variables is to be tested.
There are many such tests for measuring normality which are as follows.
Table 14: Different Tests of Normality
Graphical Method Mathematical Method/ Analytical Method
Histogram
Kolmogorov
-
Smirnov Test (Kolmogorov
,
1933)
Stem
-
Leaf Plot
Shapiro
-
Wilk Test (Shapiro and Wilk ,1965)
Box
-
and
-
Whisker Plot
Anderson
-
Darling Test (Anderson and Darling, 1952)
Probability
-
Probability/Percent
-
Percent (PP) Plot
D’Agostino
-
Pearson Omnibus Test (D’Agostino
-
Pearson, 1973)
Quantile
-
Quantile (QQ) Plot
Jarqua
-
Bera Test (Bowman and Shenton, 1975))
Detrended Probability Plot
Source: Authors own Compilation
For selection of test and method of normality, Das & Imon, 2016 deduced that analytical test of normality
is more preferable than graphical test and recommended Shapiro-Wilk Test. Razali & Wah (2011) compared four
normality tests with ten thousand samples and also deduced that Shapiro-Will test of normality is most powerful
followed by Anderson-Darling test, Lilliefors test & Kolmogorov-Smirnov test. In the present study, Shapiro-
Wilk test, Kolmogorov-Smirnov test along with histogram, PP plot, QQ plot and descriptive statistics are applied
for assessing normality in different situations. The null hypothesis for normality is that data tend to be normal.
Thus, sig./p value more than .05 is desired to accept such hypothesis. Normality of continuous variables are
desired.
Table 15: Normality of Variables
Variables
Kolmogorov-Smirnov Shapiro-Wilk
Statistic df
Sig. Remark Statistic df
Sig. Remark
V1 .270 7 .133 Normal .822 7 .066 Normal
V2 .428 7 .000 Non-Normal .564 7 .000 Non-Normal
V3 .180 7 .200 Normal .956 7 .780 Normal
V4 .240 7 .200 Normal .889 7 .272 Normal
V5 .252 7 .199 Normal .765 7 .018 Non-Normal
Source: Authors own Compilation
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 30 | Page
Normality with Kolmogorov-Smirnov and Shapiro-Wilk test of different financial parameters is shown
in the above table. All the parameters are normal except the second variable under Kolmogorov-Smirnov test.
Similar results are also drawn from Shapiro-Wilk test statistics. Further, Shapiro-Wilk test reveals that variable 5
is not normally distributed.
VIII. Regression Assumptions
Normality of Residuals
In linear regression analysis, normality of residuals is an essential assumption. Chan (2004) narrated such
assumptions quite clearly. The normality of regression equations is shown below.
Figure 1: Normality of Residuals with Histogram and PP Plot of Regression Model 1
Source: Authors own Compilation
The distribution of residuals shows that all the data points are within the histogram. The data points are
also nearer to the PP Plot. Both the pictures above infer that residuals are normally distributed. The residuals of
other models are tested in the similar way and found a normal distribution.
Table 16: Normality of Std. Residuals with Descriptive Statistics
Models Mean SD
1 .000 .993
2 .000 .988
3 .000 .991
4 .000 .986
Source: Authors own Compilation
The table above shows normality of residuals of regression models with mean and standard deviation.
Mean is zero and standard deviation is very nearer to one. It ensures that residuals of all regression models are
normally distributed.
R squared value explains the degree of variability in the dependent variable by the independent variable.
It infers about the goodness of fit of the model to the observed data. “An R-squared of 60% reveals that 60% of
the data fit the regression model”6. Further, 60% of the dependent variable variance has been affecting independent
6 https://corporatefinanceinstitute.com/resources/knowledge/other/r-
squared/#:~:text=The%20most%20common%20interpretation%20of,better%20fit%20for%20the%20
model.
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 31 | Page
variable. But difference of opinion has been observed for the reliability of this test result. It is opined that small R
square value does not always mislead and high R-square value may not be always essentially good7.
Table 17: R- squared and Adjusted R-Squared
Models R Square Adjusted R Square
1 .138 .126
2 .143 .122
3 .206 .190
4 .213 .191
5 .159 .143
6 .166 .142
Source: Authors own Compilation
All the models have low R-squared value. Researchers opined that research analysis can be proceeded
even with low R-squared value. Akossou & Palm, (2013) opined that R squared is a biased estimate. Filho et. al.
(2011) substantiated that coefficient of determination fails to draw a meaningful conclusion. Dodge (1999) added
that such value can be increased by subsequent addition of variables. Thus, other parameters like F statistics, D-
W statistics can be examined in regression analysis along with R-squared value.
Durbin-Watson (D-W) Statistics
Durbin-Watson (1950) Statistics measures auto-correlation. It is said that “the Durbin Watson (DW)
statistic is a test for autocorrelation in the residuals from a statistical regression analysis8”. Maxwell & David,
(1995) and White (1992) opined that such statistics should be within 1.5 to 2.5 so that there will be no
autocorrelation at lag 1.
Table 18: Durbin-Watson (D-W) Statistics
Models D-W Statistics
1 1.725
2 1.728
3 2.129
4 2.122
5 1.749
6 1.766
Source: Authors own Compilation
The Durbin Watson statistics of all the models are within the recommended level. Thus, it can be inferred that the
model is not affected by auto-correlation.
F-statistics
Table 19: F-statistics and Model Fit
Models F Value Sig./P value
1 11.138 .000
2 6.882 .000
3 13.458 .000
4 9.318 .000
5 10.010 .000
6 6.966 .000
Source: Authors own Compilation
7 https://statisticsbyjim.com/regression/interpret-r-squared-regression/
8 https://www.investopedia.com/terms/d/durbin-watson-statistic.asp
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 32 | Page
F statistics assumes that the regression model may not have predictive efficiency. The null hypothesis is that there
are zero regression coefficients. There are no variables affecting the target variable except the intercept or
constant. The null hypothesis must be rejected. In the above table, the null hypothesis for all the models is rejected
1% level of significance. The model is said to be fit and having some value of regression coefficients.
Test of Multicollinearity
There should not be multicollinearity issue in a regression model. Multicollinearity is a state where two
or more independent variables are highly inter-correlated with each other. The independency of the predictors is
violated. It occurs when multiple factors are correlated.9 It leads to overestimation of the results. Daoud (2017)
inferred that the correlation among dependent variables is undesired. Such problem increases the value of standard
error of the suffered coefficient. Type II error is invaded to the model. Lindner (2020) found that multicollinearity
does not lead to bias however it violates regression assumption. Detection of such issue can be made by made by
assessing tolerance level and Variance Inflation Factor (VIF). No multicollinearity is detected when tolerance
level is more than .7 and VIF is within 3.
Table 20: Collinearity Statistics
Factors Tolerance VIF
Factor 1 .942 1.061
Factor 2 .927 1.079
Factor 3 .968 1.033
Factor 4 .882 1.134
Factor 5 .910 1.099
Source: Authors own Compilation
In the above table, the variables which are derived from explorative factor analysis for regression purpose have
no multicollinearity problem as both tolerance and VIF are within the recommended value.
Homoscedasticity or Constant Variance of Residuals
Panda et al., (2020) reported that “there must be constant variance among residuals” when regression
analysis is applied. Heteroscedasticity is a problem because ordinary least squares (OLS) regression assumes that
all residuals are drawn from a population should have a constant variance (homoscedasticity)10. The plots must
be scattered across the area, then it is said that there is constant variance of residuals.
Model 1
Model 2
Fig 2: Constant Variance of Residuals
Source: Authors own Compilation
10https://statisticsbyjim.com/regression/heteroscedasticityregression/#:~:text=Heteroscedasticity%20is
%20a%20problem%20because,should%20have%20a%20constant%20variance.
Developing a Research Methodology with the Application of Explorative Factor ..
DOI: 10.9790/487X-2304022335 www.iosrjournals.org 33 | Page
The table above shows the scatter plot of residuals of model 1 and model 2. The plots are spread across
the scatter plot without forming a clear pattern. Thus, it can be inferred that there is a constant variance of residuals.
Similar inferences are to be drawn for other models also.
IX. Conclusion
The way or mean of achieving research objectives is carefully decided in this chapter. Research design
is framed. A rigorous screening is undertaken for the data set so that unengaged responses are to be ignored.
Moreover, outliers are checked with missing values. Statistical tools are selected on the basis of objective and
nature of data. Due care is taken to test the assumptions of a tool before applying it.
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