Powerpoint slides for project

Running Head: Response ! 1

Final Project

by Julia Fernandez

Professor Heeyoung Kim

Rider University

August 6, 2018.

Running Head: Response ! 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?

Running Head: Response ! 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:

Running Head: Response ! 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

Running Head: Response ! 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 determining the total

expenditure of manufacturing firms in the US.

H2: There is a relationship between the production of workers in determining the total

expenditure of manufacturing firms in the US.

Ho: There is a no relationship between production of workers in determining the total

expenditure of manufacturing firms in the US.

Running Head: Response ! 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

Running Head: Response ! 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

Running Head: Response ! 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:

Running Head: Response ! 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

Running Head: Response ! 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.

Running Head: Response ! 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:

Running Head: Response ! 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.

Running Head: Response ! 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

Running Head: Response ! 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:

Running Head: Response ! 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

Running Head: Response ! 16

is 0.0089 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 0.3869 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

Running Head: Response ! 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

Running Head: Response ! 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.

Significant of the coefficients with discussion of significance level. Which variables (if

any) appear to be useless for predicting the response variable?

Running Head: Response ! 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

Running Head: Response ! 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

Running Head: Response ! 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.

Running Head: Response ! 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.

•

Running Head: Response ! 23

Appendix:

Running Head: Response ! 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