Business Statistics: Regression and Correlation Analysis

This report explores the use of regression and correlation analysis in business statistics. It covers the estimation of relationships, interpretation of R squared, and prediction of future earnings. The impact of gender, degree, skill, and experience on earnings is also discussed.

Business Statistics

EXECUTIVE SUMMARY
The present study is based on business statistics which involves study of numbers and analysis of
numeric information with help of different data sets. The present report has undertaken the use of
correlation and regression in order to analyse and evaluate the data presented.

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................3
MAIN BODY...................................................................................................................................3
Conducting preliminary analysis of relationship among various variables................................3
Use of linear regression for estimating relationship...................................................................3
Use of multiple regression..........................................................................................................4
Interpreting R squared in model A and adjusted R squared in model B.....................................5
Comparing the coefficient of gender in model A and model B..................................................5
Predicting the earning of male and female worker with same characteristic..............................5
Two new variables......................................................................................................................6
CONCLUSION................................................................................................................................6
REFERENCES................................................................................................................................8

INTRODUCTION
Business statistics is being referred to as the use of data analysis tools in order to analyse
and interpret the data for taking decision. This is very essential for the business to manage and
use data in order to analyse it and take decision for better working of company. Thus, the current
study will outline the use of some statistical tools and techniques and it is assistive for taking the
decision.
MAIN BODY
Conducting preliminary analysis of relationship among various variables
earnings
('000
AU$) male degree skill experience
earnings ('000
AU$) 1
male 0.15001 1
degree 0.32319 -0.1362 1
skill 0.27559 0.04794 0.35366 1
experience 0.10662 0.06803
-
0.03855 -0.0425 1
With the help of the above correlation analysis, it is clear that degree is the most correlated
variable with earning. This is particularly because of the reason that level of earning is generally
dependent over the degree of the person (Liu, 2017). This simply implies that when the person
will be having high degree then their earning will be more. In the similar manner, skill is also
related to the earning. The reason underlying this fact is that when person will be skilled then
also they will be having more earning.
Use of linear regression for estimating relationship
Regression
Statistics
Multiple R 0.15001
R Square 0.0225
Adjusted R
Square 0.02131
Standard Error 1.0455
Observations 824

ANOVA
df SS MS F
Significance
F
Regression 1 20.6852 20.68525 18.924
1.53135E-
05
Residual 822 898.503 1.09307
Total 823 919.188
Coefficients
Standard
Error t Stat
P-
value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 1.44977 0.05845 24.80571
8E-
102 1.335055582 1.56449 1.33506 1.56449
male 0.32509 0.07473 4.350172
1.5E-
05 0.178405226 0.47177 0.17841 0.47177
With the above analysis of the regression it is clear that there is no significant relation between
the earning and gender. This is particularly because of the reason that significance value is more
than 0.05.
Use of multiple regression
Regression
Statistics
Multiple R 0.423
R Square 0.17893
Adjusted R
Square 0.17492
Standard Error 0.95996
Observations 824
ANOVA
df SS MS F
Significance
F
Regression 4 164.466 41.11662 44.6184
6.46273E-
34
Residual 819 754.722 0.921516
Total 823 919.188
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.91994 0.07329 12.55193 3.5E-33 0.776077247 1.0638 0.77608 1.0638
male 0.37684 0.06979 5.399395 8.8E-08 0.239846431 0.51384 0.23985 0.51384

degree 0.64069 0.07544 8.49315 9.4E-17 0.492621966 0.78877 0.49262 0.78877
skill 0.3765 0.07588 4.96171 8.5E-07 0.227556128 0.52545 0.22756 0.52545
experience 0.01218 0.00342 3.563327 0.00039 0.005471581 0.01889 0.00547 0.01889
Here the null hypothesis is being accepted as the significance value is more than 0.05. hence, this
results in selection of null hypothesis and rejecting the alternate.
Interpreting R squared in model A and adjusted R squared in model B
The R within the model A is 0.15 or 15 % whereas in model B adjusted R square is 0.17
or 17 %. This simply means that in case of model A, the correlation between the gender and
earning is only 15 %. Whereas in case of model B the adjusted R square is 17 %. So it can be
implied that Model B is a better model.
Comparing the coefficient of gender in model A and model B
The coefficient of gender is model A is 0.32 and in model B is 0.37. Hence this implies
that the model B is having more coefficient as compared to other one. With respect to the gender
discrimination it is clear that the results of both the model varies (Black, 2019). This is
particularly because of the reason that when the other variable is also included like skill,
qualification then the discrimination increases more.
Predicting the earning of male and female worker with same characteristic
Equation
Y= 0.0083X + 2.6159

Prediction of next value = 0.0083 (13) + 2.6195
= 0.1079+2.6195
= 2.7274
Female
Equation
Y= 0.3585X + 0.831
= 0.3585 (13) + 0.831
= 4.6605 + 0.831
= 5.4915
Two new variables
For the analysis of factors that influence worker earning, other variable involves
background of person and productivity level. The background of person affects the earning as
when person is not having good background then it will result in less pay to person (Anderson
and et.al., 2020). In the similar manner, the productivity level of the person also affects the
working and earning level. The reason pertaining to this fact is that when the person will not
work productively then this will result in person not getting the pay.
CONCLUSION
The above report concluded that business statistics involves various statistical techniques
which assist the company in evaluating the business. hence, this assist the company in taking

proper decisions. The above analysis included use of regression and correlation and also
regression was used to predict the future earnings.

REFERENCES
Books and Journals
Anderson, D.R. and et.al., 2020. Modern business statistics with Microsoft Excel. Cengage
Learning.
Black, K., 2019. Business statistics: for contemporary decision making. John Wiley & Sons.
Liu, Z., 2017. Teaching reform of business statistics in college and university. EURASIA Journal
of Mathematics, Science and Technology Education. 13(10). pp.6901-6907.