Applied Statistics and Forecasting: Regression and ANOVA Analysis

This report delves into the application of statistics and forecasting, employing quantitative methods to analyze empirical data and its impact on business presentation. It utilizes inferential tools such as regression analysis, factor analysis, one-way ANOVA, and cluster analysis via SPSS to explore relationships between variables. Task 1 examines the relationship between causal factors (publication, position, universities, state) and salary, revealing a moderate correlation and significant difference. Task 2 investigates the impact of size and cooperation on innovation in UK companies, identifying significant alterations and differences in innovation levels. The report concludes that statistical analysis is crucial for forecasting and decision-making, emphasizing the interdependency of variables and the importance of innovation for UK companies.

Applied statistics and Forecasting

INTRODUCTION
Statistics is a science which is related with developing and studying methods for
collecting and analyzing the empirical data. This in turn also assist in the forecasting and that is
why most of the top companies uses this tool in order to recover the business presentation. The
present study also assist to increase the information relating to the statistics and this will further
be helpful to create a better outcome in order to generate a brand image at global level. The
current study is based upon two different topics in which inferential tool will be applied that
helps to determine about usage of different tools over it.
METHODOLOGY AND DATA
It is necessary for the scholar to choose the methodology according to the research
questions which in turn assist to accomplish the set aim and objectives. The methodology for the
present study is as mentioned below:
Research type: Generally, there are two types of research i.e. qualitative and
quantitative. For the current report only quantitative research type has been adopted which in
turn deals with figures and facts and also help to understand the trend (Hacker and et.al., 2022).
In the context of present research, scholar actually uses tools and technique in order to
understand the relationship between factors. Thus, deal with figures and numbers, the selected
type has been accepted over other.
Research approach and philosophy: As per the chosen research type, scholar adopted
only interpretivism philosophy and deductive research approach that helps to determine the
issues. With the help of this approach, researcher can easily answer the research questions and
also assist to generate a better outcome (Garrison, 2022). That is why, to conclude the answer
and make the research more effective, the chosen approach will be beneficial.
Data collection: There are two ways through which the data can be collected and in the
current report, only secondary data collection methods has been used which assist to meet the set
research questions. In this, the data are already collected from the official sites and this in turn
assist meet the defined aim. Also, in order to support the results, relevant books and articles has
been selected to meet the set aim.

Data analysis: Once the data has collected, it is necessary for the researcher to analyse
the information in order to reach to a valid results. There are two ways through which the data
can be analysed which includes Thematic and SPSS. For the present research, only SPSS as a
data analysis method has been adopted in which scholar can generate the valid result. With the
help of this software, the study uses different tools that assist to create a better consequence and
answer the investigation queries. With the help of such analysis, the scholar can present the
findings in an actual way in order to reach a valid conclusion.
ANALYSIS AND FINDINGS
Task 1: relationship between casual factors and effect on probability of ability salary
Null hypothesis: There is no statistical difference between the mean value of salary and casual
factors (publication, position, universities, state)
Alternative hypothesis: There is a statistical difference between the mean value of salary and
casual factors (publication, position, universities, state)

Interpretation: With the help of model summary statistics, it has been identified that the
correlation between both variable is moderate which means that when the value of constant
factors changes, there will be 65% chances that salary affects. Also, according to R square value,
it entails that when the publication and position changes there is 43% change identified over
salary and this reflected that salary actually affected from the casual factors (Goolab, 2021).
Further, according to anova table, it has been identified that there is a significance
difference between the mean value of salary and casual factors. As a result, alternative
hypothesis is accepted over the other because the value of significance difference is 0.00 which
is lower than 0.05.
By applying Durbin Watson test whose value is 1.3 signposted that there is a positive
autocorrelation between the variables. Thus, it has been shows that both factors will run in a

similar direction. Moreover, according to scatter plot and residual statistics, it can be interpreted
that variable are constant across the predictor and thus, the observed value do not varied more
easily. Thus, it has further evaluated by collinearity statistics under a coefficient table that the
value of VIF is in between 0 to 10 in all cases rather than professor. Therefore, there is a need to
remove the outlier from professor case in order to fall the same into 0 to 10. Rest of the others
shows the positive relationship between the factors.
In accordance with the error of distribution, it can be reflected through the graphs i.e.
little circles are actually follows the normality line and as a result, there is no specific drastic
deviation identified between the factors. Also, it can be stated that there is a need to understand
the ways through which the issues can be determined and complete the same.
Task 2: Impact of casual factors like size and cooperation upon the possibility of innovation in
UK companies.
Factor analysis
With the help of factor analysis, it has been identified that there is a substantial alteration
between the sample size because the value of p is 0.00 < standard criteria i.e. 0.05. Also, as per
Kaiser Meyer test, it can be stated that the value is 0.74 which is high and that is why, the model
is adequate to calculate and this in turn determine the strong correlation between different
variables. Also, in accordance with Bartlett test of Spherecity it has been reflected that the
selected sample size entails about the valid results and that is why, it shows best outcome as
well. This in turn reflected that scholar can generate a better results and analyse the research
questions as well.

One way anova
Null hypothesis: There is no difference between the mean value of innovation and size as well as
cooperation within UK companies.
Alternative hypothesis: There is a difference between the mean value of innovation and size as
well as cooperation within UK companies.
Interpretation: By applying one way anova test, it has interpreted that there is a
difference between the mean of innovation in UK companies and casual factors because the
value of significance difference is 0.00 which is lower than standard criteria. Therefore, it can be
reflected that with the change in the casual factors, the chances of innovation among UK
companies automatically changes because the difference between the mean value is high and that
is a minor change has a direct impact over an innovation within a companies.
Cluster analysis