Running Head Response .docx

Running Head: Response
! 1
Final Project
by Julia Fernandez
Professor Heeyoung Kim
Rider University
August 6, 2018.
! 2
Background:
Manufacturing sector of USA is considered as the backbone of
economy. This sector
contributes a lot in earning foreign exchange and maintaining
the GDP of the company. As it also
plays an important role in inflation. If the goods that are
produced under this sector sell in the
market at a reasonable price than keeps stability in economy
and if the products are sell at high

prices than inflation arise that leads to create disability in the
country. As we know that United
States is renowned for its high quality manufacturing products
(Timothy E. Zimmer, 2017).
Therefore, US exported billion dollar products every year. It
contributes a lot in earning foreign
exchange that keep the reserves of country always high. Hence,
the role of manufacturing sector
plays a significant role in the development and progress of
country towards prosperity.
Description of problem:
The problems that is intended to explore in this report is that,
“how the expenditure of the
manufacturing companies are affected by number of employees
and its productivity”. As we
know that these manufacturing sector are capital intensive and
labor intensive companies that
require a lot of money and man power to operated (census.gov,
2016). Hence, every
manufacturing company struggles that how they can lower their
expenditure are kept low by
increasing the productivity of employees. Thus, this relationship
is investigated in this report. If
the companies are successful in lowering their expenses that

they will be able to earn high profits
that benefits the company and country as well.
Why this topic interests me?
! 3
There are many reason due to which I select this sector as this is
the biggest sector of
United States and my core interest is in the exploration of this
sector. I want to explore those
variables that contributes in the success of manufacturing
sector. Moreover, I want to explore
that whether number of employees have a direct impact on the
productivity of company and on
expenditure as well. This research will help in promoting
growth in this sector.
Methodology:
The methodology that is selected to investigate this topic is,
data about the manufacturing
companies of United States is excessed through the US census
that is the latest census which was
conducted in 2016.

Study unit:
The unit of study is the main body that is being analyzed in this
study. In this study the
unit of analysis is the manufacturing companies of United
Stated.
Target population:
The target population for this study is “Manufacturing firms of
United Stated”
Sample size:
There are hundreds of manufacturing firms in United States out
of these hundred state I
selected only 45 stated according to the geographical area.
Definition of variables:
! 4
There are three variables of this study that is used to analyze
the performance of
manufacturing companies. There is one dependent and two
independent variables are used in this
study. The definition of these variables are mentioned below:
Number of employees:

Employees are the human capital in any frim that help in
accomplishing business
operations. As per the size of the firm the number of employees
are hired and according to the
type of manufacturing firm as well.
Productivity of employees:
It is referred to as the assessment of the works. It is also the
measure of efficiency of
worker. There are different ways of evaluating the productivity
of workers. It can be evaluated in
terms of output of employees in a certain time period.
Expenditure of manufacturing firms:
Expenditure is the sum of the price that the company pays on
availing the product
and services of employees. The expenditure of the company
depends on many factors like prices,
elasticity of demand and number of employees as well.
Dependent variable
• The dependent variable is “Total expenditure of manufacturing
firm”.
Independent variables

• Number of employees
! 5
• Productivity of workers.
Explanation of the sampling method:
The sampling method that is used in this study is simple random
sample. This sampling
method is a subset of statistical population in which all the
elements of sample have equal
opportunity of being selected. It is the unbiased representation
of the group.
Form the independent and dependent variables the hypothesis of
the study that are
intended to investigate this relationship is described below.
H1: There is a relationship between a number of employees and
the production of
workers in determining the total expenditure of manufacturing
firms in the US.
Ho: There is no relationship between a number of employees
and the production of
workers in determining the total expenditure of manufacturing
firms in the US.

Sub-hypothesis:
H1: There is a relationship between a number of employees in
determining the total
expenditure of manufacturing firms in the US.
Ho: There is no relationship between a number of employees in
H2: There is a relationship between the production of workers
in determining the total
Ho: There is a no relationship between production of workers in
! 6
Simple Linear Regression analysis: Based on the hypothesis
simple regression analysis
is applied to predict the dependent variable.
Independent variable: Number of employees.
In this regression analysis, the independent variable that is used

is Number of employees
while the dependent variable is total expenditure.
Scatterplot with the regression line
Multiple R 0.083132454
R Square 0.006911005
Adjusted R
Square
-0.016184088
Standard Error 25067069.69
Observations 45
ANOVA
df SS MS F
Significance
F
Regression 1 1.88 1.88 0.299241 0.587186397
Residual 43 2.7 6.28
Total 44 2.72
Coefficients Standard Error t Stat P-value Lower 95% Upper
95% Lower 95.0% Upper 95.0%
Intercept 9192259.67 5238167.144 1.754861847 0.086406 -
1371511.15 19756030.49 -1371511.15 19756030.49

X Variable 1 -9.0066884 16.46472178 -0.547029493 0.587186 -
42.2109644 24.19758757 -42.2109644 24.19758757
SUMMARY OUTPUT
Regression Statistics
! 7
!
Regression line equation
The regression line equation that is developed for this variable
is,
Y= a +b X
Y = dependent variable
X = Independent variable
a = value of intercept
b = slop of equation
Y = 9.192 + -9.007*X
Slope of regression line:
The slope of regression line is the rate of change in Y with the
change in X. As we know

that Y is dependent on X. therefore the slope describes the
predicted values of Y that is given as
! 8
X. by applying the least square method of linear regression that
slop is calculated. Thus by
calculating the b with the covariance of x and y that is further
divided by the variance of X.
The slop of regression is calculated by the y – intercept when
we use under a linear
regression as the intercept is calculated by the slop. Hence the
slop of regression line is used by
applying t – test to find the significance of linear relationship
between the x and y.
The slop of regression line calculation is mentioned below:
! 9
!
Value of R:
Best-fit values

Slope -9.007 ± 16.46
Y-intercept
9.192e+006 ±
5.238e+006
X-intercept 1.02E+06
1/Slope -0.111
95% Confidence
Intervals
Slope -42.23 to 24.22
Y-intercept
-1.378e+006 to
1.976e+007
X-intercept -infinity to +infinity
Goodness of Fit
R square 0.006911
Sy.x 2.51E+07
Is slope
significantly
non-zero?
F 0.2992
DFn,DFd 1,43
P Value 0.5872
Deviation from
horizontal?

Not Significant
Data
Number of XY
pairs
45
Equation
Y = -9.007*X +
9.192e+006
! 10
The value of R shows the correlation between the observed
values and predicted values
of Y. The value of R shows that the relationship between the
variables is not significant. Hence,
we can say that number of employees and total expenditure are
not correlated with each other.
They might be other factors who affect this relationship.
Value of R 2:
Through the value of R square it is analyzed that whether there
is a significant
relationship between the variables or not. if the value of R
square is closer to 1 than there exist a

closer relationship and if it lies close to 0 than there is a week
relationship. The value of R square
is 0.005 shows that there is no significant relationship is present
between the dependent and
independent variables.
Significant of the coefficients with discussion of significance
level
To analyze the significance level if the value of F is greater
than the model is significant
and if it is less than 5 than the modal is not significant. For
greater significance level the value of
P must be low than 0.05. The value of F is 0.299241 that is less
than 5. Thus the relationship
between number of employees and expenditure is not
significant. The value of P is greater than
0.05 that is 0.0864 and 0.587 it verifies that the relationship is
not significant. The value of
coefficient is greater than significant level it shows that the
model is not significant.
The residual vs. predicted graph for the best predictor
regression. Explain the
implications.

! 11
The value of the residual shows that how the actual data points
are different from
predicted data points. Below mentioned is the residual graph
that shows how all the values are
kept at the same lines under the regression analysis.
!
But the predictor graph that is mentioned below show the
different model.
!
Which is the best predictor according to statistical analysis?
State your reasoning.
According to the statistical analysis the best predictor is
mentioned below:
! 12
!
The fit line plot shows that how the predicted variable is
applied in the dependent
variables to get the desirable results. For the best implication of

predicted value, it is evaluated
that predicted values that are calculated under the residual must
be added in order to make this
model significant.
Independent variable: productivity of workers.
In this regression analysis, the independent variable that is used
is productivity of
workers while the dependent variable is total expenditure.
! 13
!
Scatterplot with the regression line
!
Regression line equation
The regression line equation that is developed for this variable
is,
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.094435286
R Square 0.008918023
Adjusted R Square -0.014130395

Standard Error 25041726.79
Observations 45
ANOVA
df SS MS F Significance F
Regression 1 2.42 2.42 0.386925614 0.537204354
Residual 43 2.6 6.27
Total 44 2.72
Coefficients Standard Error t Stat P-value Lower 95% Upper
95% Lower 95.0% Upper 95.0%
Intercept 9531853.868 5308426.096 1.795608283 0.07958623 -
1173607.63 20237315.37 -1173607.63 20237315.37
X Variable 2 -15.1204436 24.30808757 -0.622033451
0.537204354 -64.14237419 33.90148698 -64.14237419
33.90148698
! 14
Y= a +b X
Y = dependent variable
X = Independent variable
a = value of intercept
b = slop of equation
Y= a +b X
Y = -15.12*X + 9.532e+00

Slope of regression line:
The slop of the regression line predicts the value of Y from the
given value of X. with the
help of least square method the slop of linear regression is
calculated. With the help of value of Y
– intercept the slop of regression is calculated. Furthermore, the
t – test help in finding the
significant relationship.
The slop of regression line calculation is mentioned below:
! 15
!
Value of R:
The value of R shows the correlation between the observed
values and predicted values
of Y. The value of R shows that the relationship between the
variables is not significant. Hence,
we can say that productivity of workers and total expenditure
are not correlated with each other.
Value of R 2:

Through the value of R square it is analyzed that whether there
is a significant
relationship between the variables or not. If the value of R
square is closer to 1 than there exist a
closer relationship and if it lies close to 0 than there is a week
relationship. The value of R square
! 16
is 0.0089 shows that there is no significant relationship is
present between the dependent and
independent variables.
level
To analyze the significance level if the value of F is greater
than the model is significant
and if it is less than 5 than the modal is not significant. For
greater significance level the value of
P must be low than 0.05. The value of F is 0.3869 that is less
than 5. Thus the relationship
between productivity of workers and expenditure is not
significant. The value of P is greater than
0.05 that is 0.0795 and 0.5372 it verifies that the relationship is
not significant. The value of

coefficient is greater than significant level it shows that the
model is not significant.
The residual vs. predicted graph for the best predictor
regression.
The value of the residual shows that how the actual data points
are different from
predicted data points. Below mentioned is the residual graph
that shows how all the values are
kept at the same lines under the regression analysis.
!
But the predictor graph that is mentioned below show the
different model.
X Variable 1
Residual Plot
R
e
s
id
u
a
ls
0
13

25
38
50
X Variable 1
0 30000 60000 90000 120000
! 17
!
!
The graph of line fit plot shows the difference between residual
plot and predicted value
of y. This graph will be helpful in identifying the gap and the
necessary change will be
implemented.
Multiple Regression:
Regression line equation:
Under the multiple regression analysis, regressions line
equation is mentioned as follow:
Y = a +b1X1 + b2X2

Predicted Y
-2500000
0
2500000
5000000
7500000
10000000
0 13 25 38 50
X Variable 1
Line Fit Plot
Y
0
45000000
90000000
135000000
180000000
X Variable 1
0 200000 400000 600000 800000
Y

Predicted Y
! 18
Y = a +9.192 + -9.007*X +-15.12*X
!
Value of Adjusted R 2:
The value of adjusted r square is used in analyzing the
relationship between the
dependent and independent variables of the study. The value of
this R square is between the 0
and 1. If the value is identified as closer to 1 it means that
relationship is strong and if it is closer
to zero than it means that relationship is weak. In this analysis
the value of R square is calculated
as 1.02 that is close to one its means that there is close
relationship between the variables of
study. The values that are calculated form simple regression is
close to 0 shows that, the model
that is presented is insignificant. But the multiple regression
shows that modal is significant.
level. Which variables (if

any) appear to be useless for predicting the response variable?
! 19
As per the analysis of the coefficient with the significant level.
The P value is equal to
0.05 that shows the significance of study. Hence, it is evaluated
that independent variables that
are the number of employees and productivity of workers
defines the relationship with
expenditure of company.
Significant test of F - statistics and interpret:
The value of F – statistics tests the significance level of studies.
the F statistics of this
study is greater than 5 that is 0.767 for number of employees
and 8.093 for productivity of
workers that shows that model is significant and there exists a
positive relationship between
dependent and independent variable.
Make sure to check the residual plot to verify the model
assumptions for the best fit
model.

!
X Variable 1
Residual Plot
R
e
s
id
u
a
ls
-40000000
0
40000000
80000000
120000000
160000000
X Variable 1
0 300000 600000 900000 1200000
! 20
!
!

!
Conclusions
X Variable 1
Line Fit Plot
Y
-45000000
0
45000000
90000000
135000000
180000000
X Variable 1
0 600000 1200000
Y
Predicted Y
X Variable 2
Residual Plot
R
e
s
id
u
a

ls
-40000000
0
40000000
80000000
120000000
160000000
X Variable 2
0 200000 400000 600000 800000
X Variable 2
Line Fit Plot
Y
-45000000
0
45000000
90000000
135000000
180000000
X Variable 2
0 200000 400000 600000 800000
Y
Predicted Y

! 21
From the analyses of the multiple regression, it is evaluated that
there is a significant
relationship between the dependent and independent variables.
In order words, we can say that,
“There is a relationship between a number of employees and the
production of workers in
determining the total expenditure of manufacturing firms in the
US.” The number of employees
have a significant impact on the expenditure of company. As the
number of employees increase
the expense of the company also increase and the productivity
of workers also increase. Hence,
this relationship states that higher the number of workers,
greater will be the productivity and
higher will be the expenses of company.
The problems that is investigated in this study, it is evaluated
that for achieving greater
productivity the number of employees should be increased that
will help the company to expand
their products in different companies.

! 22
References
• census.gov. (2016, 1 1). Manufacturing Firms . Retrieved from
census.gov: https://
www.census.gov/data/tables/2016/econ/asm/2016-asm.html
• Timothy E. Zimmer, P. K. (2017). Lean manufacturing: The
production employment and
wages connection. Indiana Business Review, 92(1), 1-10.
•
! 23
Appendix:
! 24
Id2 Year
Geographic area
name

Number of
employees
Production
workers average
for year
Total capital
expenditures
($1,000)
1 2016 District of Columbia 1259 813 168317599
2 2016 Hawaii 11513 7149 4187468
3 2016 Alaska 12178 10176 204082
4 2016 Montana 16697 11238 1924308
5 2016 New Mexico 21747 14700 1994511
6 2016 North Dakota 22862 16912 13062872
7 2016 Delaware 25434 17901 1534982
8 2016 Vermont 27420 18641 1452456
9 2016 Rhode Island 36081 23745 500411
10 2016 Nevada 41356 27759 9730
11 2016 South Dakota 44094 32491 3927971
12 2016 Maine 49710 35983 4450840
13 2016 Idaho 55774 41205 129621
14 2016 New Hampshire 65553 39464 1342579
15 2016 Maryland 91791 56258 6681908
16 2016 Nebraska 92945 70717 7046728
17 2016 Louisiana 113914 80129 3658211
18 2016 Colorado 121069 79052 2211855
19 2016 Oklahoma 121220 89068 3904222
20 2016 Mississippi 130537 103082 8699895
21 2016 Arizona 136946 82409 438790
22 2016 Arkansas 145733 116757 1153209
23 2016 Kansas 154684 110902 2369195
24 2016 Connecticut 155062 87968 7409725

25 2016 Oregon 160128 108945 3419845
26 2016 Iowa 203835 147954 1589847
27 2016 New Jersey 210291 139870 2823733
28 2016 South Carolina 213050 159797 642828
29 2016 Massachusetts 223996 131020 1109775
30 2016 Kentucky 230763 178593 456874
31 2016 Alabama 234803 176679 569796
32 2016 Missouri 245352 182878 2738486
33 2016 Florida 270180 179959 502613
34 2016 Minnesota 297770 197099 5140968
35 2016 Tennessee 308966 228500 5152963
36 2016 Georgia 351951 265733 331143
37 2016 New York 395129 261216 10755438
38 2016 North Carolina 411050 303771 2273823
39 2016 Indiana 476417 357501 2623293
40 2016 Pennsylvania 522221 362007 7348275
41 2016 Illinois 538183 370965 346802
42 2016 Michigan 555005 398946 3549962
43 2016 Ohio 642945 460781 433012
44 2016 Texas 725255 493691 5121563
45 2016 California 1119896 706390 19745490

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