Regression and Econometric Analysis

The given assignment involves solving problems related to regression analysis and econometric techniques. Task 1 requires analyzing the relationship between size and turnover using a regression model. Task 2 involves calculating the economic order quantity (EOQ) and its effect on carrying cost per order. Task 3 presents a scenario where male and female gross annual earnings from 2009 to 2016 across public and private sectors are compared. The conclusion highlights the reliability of results generated by the regression model and emphasizes the importance of focusing on the validity of the model in business decision-making.

STATISTICS MANAGEMENT

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
TASK 1............................................................................................................................................1
(a)Identifcation of change in gross annual earnings in public and private sector since 2009 and
pay gap across genders................................................................................................................1
TASK 2............................................................................................................................................4
(a)Ogive chart and computation of mean as well as standard deviation.....................................4
(b) Comparison of earning of two regions...................................................................................6
(a)Area and average weekly turnover scatter diagram and reltionship between them................7
© Equation used for making prediction.....................................................................................10
(e) Statistical validity of model..................................................................................................10
TASK 3..........................................................................................................................................11
(a)Number of delieveries made each year by firm....................................................................11
(b) Number of bootles of olive oil sold on each delievery........................................................12
©Economic order quantity.........................................................................................................12
(d) Comparison of cost with change in EOQ.............................................................................12
TASK 4..........................................................................................................................................13
(a)Male and female gross annual earning from 2009 to 2016 across public and private sector13
(b) Ogive chart on cumulative percentage of employees VS hourly earnings..........................14
© Size VS turnover....................................................................................................................14
CONCLUSION..............................................................................................................................15
REFERENCES..............................................................................................................................16
Figure 1Trend of gross income across education and finance industry...........................................3
Figure 2Ogive chart.........................................................................................................................4
Figure 3Relationship between size and turnover.............................................................................7

Figure 4 Trend in gross income across gender and public as well as private sector.....................13
Table 1Variation in gross annual earning of pblic and private sector.............................................1
Table 2Data for Ogive.....................................................................................................................4
Table 3Calculation of mean.............................................................................................................5
Table 4Input for computing standard deviation...............................................................................5
Table 5Calculation of standard deviation........................................................................................6
Table 6Number of bootles transported..........................................................................................12
Table 7Calculation of economic order quantity............................................................................12
Table 8 Cost at different level of EOQ..........................................................................................12

INTRODUCTION
Statisitics is the one of the most common discipline that is used by managers and help
them in analyzing facts and making prudent decisions. In current report, facts and figures related
to public and private sector in respect to male and female is analyzed in varied ways. Apart from
this, regression method is applied on retail shop data and relationship is identified between
variables. Validity of model is measured and reliability of results is determined. At end of report,
charts are prepared and same are interpreted in proper manner.
TASK 1
(a)Identifcation of change in gross annual earnings in public and private sector since 2009 and
pay gap across genders
Table 1Variation in gross annual earning of pblic and private sector
2009 2010 2011 2012 2013 2014 2015 2016
Public
5586
2
5737
7
5785
0
5845
2
5987
9
6058
3
6158
5
6206
4
Private
4691
3
4653
2
4679
8
4801
8
4889
9
4945
9
5028
4
5193
0
% Change in annual earning of
public sector 3% 1% 1% 2% 1% 2% 1%
% Change in annual earning of
private sector -1% 1% 3% 2% 1% 2% 3%
Interpretation
Facts revealed that almost most of times gross annual earnings change almost at same
pace across public and private sector. It can be observed that in year 2010 relative to previous
year annual earning decline in private sector by -1% and same increased to 3% in case of public
sector. However, from 2011 to 2015 change almost remain same in public and private sector.
trend get inversed in terms of change in earning as it can be seen that annual earning changed by
1% in 2016 in comparison to 2015 and same increased to 3% in case of private sector. It can be
concluded that almost at same rate gross income change in public and private sector.
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2009 2010 2011 2012 2013 2014 2015
0
5000
10000
15000
20000
25000
30000
35000
40000
Income level across gender and sectors
Public sector male Private sector male
Public sector female Private sector female
Figure 1Public and private sector male and female
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2009 2010 2011 2012 2013 2014 2015
0
5000
10000
15000
20000
25000
30000
35000
40000
Income level on yearly basis across sector and
gender
Public sector male Private sector male
Public sector female Private sector female
Figure 2Public and private sector male and female
Male
200
9
201
0
201
1
201
2
201
3
201
4
201
5
201
6
Median gross annual earnings
Public sector
306
38
312
64
313
80
318
16
325
41
328
78
336
85
340
11
Private sector
273
62
270
00
272
33
277
05
282
01
284
42
288
81
296
79
Total
580
00
582
64
586
13
595
21
607
42
613
20
625
66
636
90
Female
Median gross annual earnings
Public sector
252
24
261
13
264
70
266
36
273
38
277
05
279
00
280
53
Private sector
195
51
195
32
195
65
203
13
206
98
210
17
214
03
222
51
Total
447
75
456
45
460
35
469
49
480
36
487
22
493
03
503
04
Change in pay across gender (Total of
male-Total of female)
132
25
126
19
125
78
125
72
127
06
125
98
132
63
133
86
Interpretation
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Most of years it is observed that change in gender pay gap reduce which means that gap
that exist between male and female reduced in past couple of years consistently. However, in
year 2015 and 2016 this change get increased at rapid rate which is not good. hence, it can be
said that government need to handle entire situation because by doing so such kind of situations
can be controlled and prevented from occurance.
TASK 2
(a)Ogive chart and computation of mean as well as standard deviation
(1)
Table 2Data for Ogive
F CF
Below 10 8 8
10 but under 15 22 30
15 but under 20 24 54
20 but under 25 14 68
25 but under 30 12 80
30 but under 40 14 94
40 but under 50 6 100
Below 10 10 but under
15 15 but under
20 20 but under
25 25 but under
30 30 but under
40 40 but under
50
0
20
40
60
80
100
120
8
30
54
68
80
94 100
Chart Title
Figure 3Ogive chart
Interpretation
Plotting of cumulative frequency is done in Ogive chart as it can be observed that chart is
moving upward. There are 8% candidates that have salary less then 10. After this level consistent
increase is observed in number of respondents that comes in group of 10 to 15 and 15 to 20. CF
increased to 30 and 54 across these mentioned groups. Estimated median hourly earning amount
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is 14 because above this number there are three observations and below this number there are
three observations. Hence, due to this reason range 20 to 25 is considered as median range.
Quartile value at 0.50 and median value is same. Range below10 comes in first quartile and in
third quartile range 25 to 30 may come. In last and final quartile 30 to 40 category comes. In this
way, entire data is distributed in different quartiles.
(2) Mean and standard deviation
Table 3Calculation of mean
F CF
Mid
point FX
Below 10 8 8 5 40
10 but under 15 22 30 17.5 385
15 but under 20 24 54 25 600
20 but under 25 14 68 32.5 455
25 but under 30 12 80 27.5 330
30 but under 40 14 94 35 490
40 but under 50 6 100 45 270
100 2570
Mean 25.7
Interpretation
Mean value is 25.7 which means that on average basis hourly earning that is earned by
individuals is 15 to 20. This means that most of individuals are earning an amount of minimum
of 15 and maxcimum of 20 in this range. This table also reflect that there are very small number
of respondents that are earning above mean value.
Table 4Input for computing standard deviation
F CF
Mid
point FX X^2 F*X^2
Below 10 8 8 5 40 25 200
10 but under 15 22 30 17.5 385 306.25 6737.5
15 but under 20 24 54 25 600 625 15000
20 but under 25 14 68 32.5 455
1056.2
5 14787.5
25 but under 30 12 80 27.5 330 756.25 9075
30 but under 40 14 94 35 490 1225 17150
40 but under 50 6 100 45 270 2025 12150
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100 2570
660490
0
Mean 25.7 660.49
Table 5Calculation of standard deviation
F*X^2 660.49
F*X*2 1320.98
Sum of frequency 100
2641.96
26.4196
-0.7358
661.2258
STDEV 25.71431
Interpretation
Standard deviation reflect the deviation that can be observed in case of specific variable.
Value of standard deviation is only 25 which reflect that at very slow rate values of variable is
deviating from their mean value. Hence, it can be concluded that majority of individuals that are
part of sample are receiving same amount of salary.
(b) Comparison of earning of two regions
It can be seen from table that value of median is and mean value is 16.75 as well as
standard deviation value is equal to 7.40. On other hand, on analysis of data it is identified that
mean is 25.7 and median value is 14 followed by standard deviation of 27.71. This means that in
case of South East of England high amount of salary is given relative to North East England.
However, deviation in salary is also high in South East of England.
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(a)Area and average weekly turnover scatter diagram and reltionship between them
0 2 4 6 8 10 12
0
5
10
15
20
25
30
f(x) = 0.0133333333333334 x + 3.02666666666667
f(x) = − 0.0727272727272727 x + 18.8
Regression formula
Size (S) Linear (Size (S))
Turnover Linear (Turnover)
Figure 4Relationship between size and turnover
Interpretation
Very strong relationship appear between size and turnover of the retail center. It can be
observed that with increase in size turnover value also increased and when size reduced turnover
also get reduced. This reflect that there is strong coorelation among both variables. However, in
last part of chart it can be seen that size and turnover are moving in inverse direction. Proportion
of such kind of data points is ver low in data set and this reflect that there are few cases where
trend does not match to each other. Apart from this, in all cases size and turnover are moving in
same trend.
(b) Coorelation cofficient r
Regression Statistics
Multiple R 0.913767
R Square 0.834971
Adjusted R
Square 0.814342
Standard Error 0.437532
Observations 10
ANOVA
df SS MS F
Significan
ce F
Regressi 1 7.74852 7.7485 40.476 0.000218
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on 8 28 22
Residual 8
1.53147
2
0.1914
34
Total 9 9.28
Coefficie
nts
Standar
d Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.202177
0.47603
4
0.4247
11
0.6822
39 -0.89556
1.2999
12
-
0.8955
6
1.2999
12
Size (S) 0.15749
0.02475
4
6.3620
93
0.0002
18 0.100406
0.2145
74
0.1004
06
0.2145
74
RESIDUAL OUTPUT
Observati
on
Predicted
Turnover
Residua
ls
1 3.666965
-
0.36697
2 2.092061
-
0.09206
3 2.564533
-
0.06453
4 3.351985
0.44801
5
5 4.139437
-
0.03944
6 3.981946
-
0.48195
7 1.777081
0.02291
9
8 4.296927
0.70307
3
9 2.092061
0.40793
9
10 3.037004 -0.537
PROBABILITY
OUTPUT
Percent
ile
Turnov
er
5 1.8
15 2
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25 2.5
35 2.5
45 2.5
55 3.3
65 3.5
75 3.8
85 4.1
95 5
8 10 12 14 16 18 20 22 24 26 28
0
1
2
3
4
5
6
3.3
2 2.5
3.8 4.1
3.5
1.8
5
2.5 2.5
Size (S) Line Fit Plot
Turnover
Predicted Turnover
Size (S)
Turnover
0 10 20 30 40 50 60 70 80 90 100
0
2
4
6
Normal Probability Plot
Sample Percentile
Turnover
Interpretation
Value of multiple R is 0.91 and this means that there is direct relationship between
dependent and independent variables. Correlation value maximum value always remain 1 and
minimum value always remain -1 (Poca, 2015). If coorelation value is in range of 0 to 1 then it
means that there is positive relationship between dependent and independent variable. On other
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hand, if coorelation value is negative then this reflects that there is negative relationship between
both dependent and independent variables. In model it can be observed that coorelation value is
0.91 which is nearby to 1 and this measnt that there is strong and positive relationship between
both size and turnover. This means that both size and firm profitability are related to each other.
It can be said that if firm will increase size area then profitability will certainly increase.
© Equation used for making prediction
Regression equation is commonly used for making prediction. In the equation basically
there are cofficients and same reflect change that can be observed in dependent variable with
change in independent variable. There are x variable in equation and by placing value in it
prediction is made about the variable. Regression equation for variable is given below.
Turnover= a+bsize of each outlet
(d) Prediction of turnover when floor size is 30
When outlet size is 30 turnover predicted value is 4.92. In order to make this prediction
regression equation is used which is Y=0.20+0.15*30= 4.92. On average floor size is 18.4 and
average of turnover is 3.1. On the basis of prediciton it can be said that if floor size above
average will increase consistently then it is certain that good amount of profit will be earned in
the business. Regression equation is considered as powerful medium of making prediction
because it clearly reveal that with change in single unit of independent variable what amount of
variation will comes in dependent variable.
(e) Statistical validity of model
Statistical validity of model is measured in many ways. Regression analysis is one of the
most important approach that is used to measure the relationship that exist between dependent
and independent variable. In order to measure satiatistical validity of model first of all R square
value is taken in to account which is 0.83 and this means that in most of cases actual values of
dependent variable and predicted values of turnover remain at same point. This can be observed
from the line of best fit plot.
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8 10 12 14 16 18 20 22 24 26 28
0
1
2
3
4
5
6
3.3
2 2.5
3.8 4.1
3.5
1.8
5
2.5 2.5
Size (S) Line Fit Plot
Turnover
Predicted Turnover
Size (S)
Turnover
Actually, it is always not necessary that if any model have higher p values then it is
significent as in study that is related to psycology it is observed that different people have
different thinking and due to this response does not always goes in specific direction and due to
this reason less data points match predicted values. If errors are in vicinity to lit of best fit then
also model is considered significent and it is assumed that assumptions are fulfilled (What is
linear regression, 2017). In present case, most of data points and predicted values match to each
other and due to this reason there is high value of R sqaure apart from this those errors that are
not in line of best fit are nearby to it. Hence, it can be said that model is significent and it is valid
model.
Other assumption tha is usually made in regression is that errors must have feature of
homoscadisticity which means there must be similarity in variance above and below line of best
fit. This assumption is also fulfilled by the model as it can be observed that errors are not in
funnel shape and at same rate they are above and below line of best fit (Yalcin and et.al., 2011).
In reality predicted values are on line of best fit and due to this reason assumption of
homodasticity in error also fulfilled. This again reflect that model is valid and its results are
reliable.
Theoritically, if there is independent behaviour in error then it is assumed that p value
computed for independent variable is valid. It can be observed from the chart given above that
predicted data points are specifically not moving in single direction which means that errors are
independent from each other. Due to independence in errors it can be said that value of T is not
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inflated and p value computed for model and independent variables is correct (Curran-Everett
2011). This proved that model is valid and one can completely rely on validity of its results.
There is homodascticity in model and this means that there is no presence of outliers in
data set and this also enhance validity of results that are obtained on the model. Value of level of
significence is 0.00=0.00 which means that with change in size floor turnover value also changed
significently.
TASK 3
(a)Number of delieveries made each year by firm
In order to answer this question it is assumed that firm have 10% market share and it is
making delievery of 45000 in a year.
(b) Number of bootles of olive oil sold on each delievery
Table 6Number of bootles transported
Annual demand 45000
Number of trips 30
Number of bottles in each delivery 1500
Interpretation
Number of bottles transported in each delievery are 1500. In order to compute number of
trips number of days in year is divided by 12 which is number days within which trip is made to
supermarket.
©Economic order quantity
Table 7Calculation of economic order quantity
Quantity 45000
Cost per order 2
Carrying cost per order 0.5
EOQ 600
Interpretation
Economic order quantity reflect number of units that can be purchased while keeping
inventory cost down. Economic order quantity value is 600 which means that on average basis
there may be stock of 600 items in inventory so that cost can be controlled.
(d) Comparison of cost with change in EOQ
Table 8 Cost at different level of EOQ
Quantity 45000 45000 45000 45000 45000
Cost per order 2 2 2 2 2
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Carrying cost per order 0.5 0.52 0.54 0.56 0.58
EOQ 600 588.3484
577.350
3 566.9467 557.086
Interpretation
Carrying cost at different level of EOQ will be different. In case of EOQ 588 cost is 0.52
and same is 0.56 in case EOQ is 566. This means that with increase in EOQ carrying cost per
order will reduce.
TASK 4
(a)Male and female gross annual earning from 2009 to 2016 across public and private sector
2009 2010 2011 2012 2013 2014 2015 2016
0
10000
20000
30000
40000
50000
60000
70000
Public sector male
Private sector male
Public sector female
Private sector female
Figure 5 Trend in gross income across gender and public as well as private sector
Interpretation
In case of private sector females have very low income level in past years but currently
they are earning very high amount then males. In public sector males are earning good amount of
money then females. In case of private sector also similar trend is observed. Hence, male are
earning more gross income then females.
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(b) Ogive chart on cumulative percentage of employees VS hourly earnings
Below 10 10 but under
15 15 but under
20 20 but under
25 25 but under
30 30 but under
40 40 but under
50
0
20
40
60
80
100
120
8
30
54
68
80
94 100
Chart Title
Figure 5Ogive chart
Interpretation
Ogive chart is indicating that at different level of income cumulatively number of
employees increase. This increase is fast and stable as well as decline in range of 0 to 20, 20 to
40 and 40 to 50.
© Size VS turnover
0 2 4 6 8 10 12
0
5
10
15
20
25
30
3.3 2 2.5 3.8 4.1 3.5 1.8
5
2.5 2.5
22
12
15
20
25 24
10
26
12
18
Chart Title
Size (S) Turnover
Figure 6Relationship between size and turnover
Interpretation
Results are reflecting that size and turnover are highly related to each other and both
almost move in same direction. Hence, both variables have close relation and size have impact
on turnover.
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CONCLUSION
On the basis of above discussion it is concluded that males are receiving more salary then
females across all sectors whether it is private or public. Regression model geenrate reliable
results and it is according to assumptions of linear regression and due to this reason there is
reliability of results that will be produced by model. It is concluded that it is easy to apply any
statistical method on data but reliability of results and validity of model is the one of the major
area where managers need to focus in order to ensure that right decisions are made in business.
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REFERENCES
Books and Journals
Zealand, S.N., 2013. Census QuickStats about culture and identity. Wellington: Statistics New
Zealand.
Poca, O.C., 2015. Modelos de Regresión Binaria Bayesiana Power y Reciprocal Power. Revista
Varianza. 11. pp.10-15.
Curran-Everett, D., 2011. Explorations in statistics: regression. Advances in physiology
education. 35(4). pp.347-352.
Yalcin, A. and et.al., 2011. A GIS-based comparative study of frequency ratio, analytical
hierarchy process, bivariate statistics and logistics regression methods for landslide
susceptibility mapping in Trabzon, NE Turkey. Catena. 85(3). pp.274-287.
Online
What is linear regression, 2017. [Online]. Available through:<
http://www.statisticssolutions.com/what-is-linear-regression/>. [Accessed on 11th Octomber
2017].
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