Statistical Methods in Business & Economics - Final Assignment Report

This assignment on statistical methods in business and economics addresses three key questions. The first question focuses on estimating the correlation coefficient from a provided scatter plot, explaining the concept of correlation, and differentiating between positive and negative correlations. The second question delves into index numbers, their types (price, quantity, value), and the use of weighted indexes such as Laspeyres and Paasche, along with real-life examples like the Producer Price Index and Consumer Price Index. The final question explores various statistical tests, including independent t-tests, Mann-Whitney tests, ANOVA, paired t-tests, repeated measures ANOVA, Pearson's correlation coefficient, simple linear regression, and logistic regression, detailing their applications and providing relevant examples. The assignment supports its arguments with appropriate references and bibliography.

Running head: STATISTICAL METHODS IN BUSINESS & ECONOMICS
Statistical Methods in Business & Economics
Name of the Student:
Name of the University:
Author Note:

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Table of Contents
Answer to Question 1.................................................................................................................2
Answer to Question 2.................................................................................................................3
Answer to Question 3.................................................................................................................4
Reference and Bibliography.......................................................................................................7

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Answer to Question 1.
The correlation coefficient has a range of –1 to +1. There is a positive correlation
between two variables when the correlation coefficient value is greater than 0. Negative
correlation between two variables have the value of correlation coefficient less than 0.
Negative correlation is identified when a rise in the variable reduces other variable. Again,
positive correlation shows a rise in the variable raise the value of the other variable. There are
three types of correlation depending on the strength of correlation (Ly, Marsman &
Wagenmakers 2018). These are weak correlation, moderate correlation and strong
correlation. For weak correlation the absolute value is less than 0.2. For strong correlation the
absolute value is greater than 0.7. For moderate correlation the absolute value is between 0.2
and 0.7. The scatter plot is widely used in order to visualise the data where dots are used to
present the values acquired from two variables. Each data point presents the value of the
variable at certain value of the other variable. This plot is used for presenting the relationship
between two variables. The general rule for plotting variables is that the dependent variable
should be plotted on the y axis and the independent variable on the x-axis. This plot is also
known as correlation plot as these visualises the correlation between two variables.
Figure 1: Scatter plot
The above diagram is a scatter plot where the y-axis ranges between 0 and 50 and the
x-axis ranges between 10 and 45. From the plot it is found that when x is 15 y is in between

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30 to 40. When x is raised by 10 units that is x is 25 then y is 20. Finally when x is hovering
around 40, y is near about 10. This shows the rise in x reduces the value of y. Hence it can be
said that the above scatter plot shows a negative correlation between x and y as the rise in x
reduces the value of y and vice versa. A trend line can be drawn on the scatter plot which
follows the rule of minimising the distance from each scatter plot. For strong correlations the
scatter points hover around the straight lien or stick to the straight line. The weak correlation
is found when the scatter points are spread far from the straight line. Now, if a trend line is
drawn with respect to the scatter points then it will be seen that scatter points are not far from
the trend line (Bluman, 2013). This implies that the correlation is strong. It can be concluded
that the correlation between those variables lies between -1 and -0.7. In other words, it can be
said that there is a strong negative correlation between x and y.
Answer to Question 2.
An index number compares the price or quantity or both with the standard value or
the base value. There are different types of Index numbers such as price index which
calculates the change in price over a certain range of time, quantity index which calculate the
changes in volumes of commodities and value index which compares the monetary value of
production. Except these there are simple index that shows the relative change and weighted
index (Rao & Selvanathan, 2016). There are two weighted Indexes which are Lapeyre’s
Index and Paasche’s Index.
1. Lapeyre’s Index considers quantitative data only from the base year to compare prices
over time.
2. The Lapeyre’s Index does not show the change in the pattern over time. This may
include the overweight goods for the goods that has rising prices.
3. The Paache’s Index considers the quantitative data from the current year. For this, it
shows the pattern of current buyings.

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4. The Paache’s Index needs the prices to compute again and again for each year. As it
considers only the current price.
5. The Paache’s Index does not show the change in current period. This may include the
overweight goods for the goods that has declining prices.
6. Fisher’s Index is the ideal index that omits the shortcomings of the Laspeyres and
Paasche indexes. This simply compares the prices over time.
There are few real life examples of indexes that deals with the time series data to present
the prices and quantities. Producer price index is a group of indexes which presents the
average change in price over time from the view of seller (Bairoch, 2013). Here, the price is
indicated to the price that is received by the domestic producers. Consumer price index is the
comparison of consumption of two years.
There are few indexes that are widely used in economics to compare variables that have
too many numerical values and also it is used in case of time comparisons. For example, there
is an economist who wants to trace the variations of cost of living for last 6 years. Assume,
the base year that is the first year is 2013 and the cost of an American family is $30000 to
afford the basics of livelihood. Now, in the last few years that $30000, the average cost
turned into $35000. This is raised in 6 years and has increased exponentially. Now, $30000 is
considered as the base number and it is set to 100. Now, the increased amount is scaled down
to the same as base number. Here, the value $35000 is changed to 1.667 which implies that
66.7% increase is found from 2013.
Answer to Question 3.
There are several statistical hypothesis tests which are applied to depending on the
hypothesis and the type of data. Some of the tests are discussed below:

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Independent t-test: This independent test is conducted to compare the average value of two
independent groups if the variables are nominal and scale or one variable is scale and other is
binary. The data must be normally distributed.
Mann-Whitney test/Wilcoxon rank sum: The assumptions of this test are similar to
Independent t-test, however there is a difference which is the Wilcoxon rank sum test is
applied when the data is ordinal or skewed.
One-way ANOVA: The test is applied to compare the average value of three or more than
three independent groups while the variables are nominal and scale. The non-parametric test
for the same is Kruskal-Wallis test.
The investigator wants to know the effect of three different types of treatments for a
single symptom and each of the treatment group is independent to each other. The effect is
captured with newly created index number (Cardinal & Aitken, 2013). Here, one-way
ANOVA will be applied to find out the mean differences among the index number for each
treatment. The difference will be identified by the value of F-stat and its p-value.
Paired t-test: The test is applicable only when the hypothesis is to check the difference of
average value of paired samples while the variables are scale and time or conditional
variable. The non-parametric test for the same is Wilcoxon signed rank test.
The researcher wants to now the effect of his new experimental treatment for a
particular disease (Coman et al. 2013). Now, the researcher takes the sample before the
treatment and after treatment. These two groups will be included in the paired t-test in order
to check the association between these two groups.
Repeated measures of ANOVA: This test is conducted to compare three or more than three
measurement on the same subject while the variables are scale and time or conditional
variable. The non-parametric test for the same is Friedman test.

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Pearson’s Correlation Coefficient: This indicates the correlation between two variables.
The variables must be continuous. The non-parametric test for the same is Spearman’s
Correlation Coefficient.
A very simple example of this particular technique is that if the researcher wants to
find out the relation between age and the bold pressure of the respondent, the researcher
should check the correlation between them (Wang, 2013).
Simple Linear regression: This is used to predict a variable depending on other variables or
finding for significant relationship while the depending variable is scale and the other
variables could be any form (De Los Campos et al. 2013). For the non-normal data,
transformation of data is needed.
The simple linear regression can be used in case of predicting the sales or production
depending on the price, demand, cost of raw materials and the experience of the manager.
Logistic Regression: This is used to predict a variable depending on the other variables or
finding for significant relationship while the depending variable is nominal or binary and the
other variables could be in any form. For the non-normal data, the transformation of data is
required.
The logistic regression model is often used to find out the probability of the outcome
from the dependent variable depending on the independent variables (Gim & Ko, 2017).
Suppose, the manufacturing unit wants to know if they should continue the production
depending on the variables like cost of the raw materials, demand for the production, supply
of the production and age of the manager.

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Reference and Bibliography
Bairoch, P. (2013). The economic development of the Third World since 1900. Routledge.
Beseoglu, K., Etminan, N., Steiger, H. J., & Hänggi, D. (2014). The relation of early
hypernatremia with clinical outcome in patients suffering from aneurysmal subarachnoid
hemorrhage. Clinical neurology and neurosurgery, 123, 164-168.
Bluman, A. G. (2013). Elementary statistics: A step by step approach: A brief version (No.
519.5 B585E.). McGraw-Hill.
Cardinal, R. N., & Aitken, M. R. (2013). ANOVA for the behavioral sciences researcher.
Psychology Press.
Coman, E. N., Picho, K., McArdle, J. J., Villagra, V., Dierker, L., & Iordache, E. (2013). The
paired t-test as a simple latent change score model. Frontiers in psychology, 4, 738.
De Los Campos, G., Hickey, J. M., Pong-Wong, R., Daetwyler, H. D., & Calus, M. P. (2013).
Whole-genome regression and prediction methods applied to plant and animal breeding.
Genetics, 193(2), 327-345.
Gim, T. H. T., & Ko, J. (2017). Maximum likelihood and firth logistic regression of the
pedestrian route choice. International regional science review, 40(6), 616-637.
Ly, A., Marsman, M., & Wagenmakers, E. J. (2018). Analytic posteriors for Pearson's
correlation coefficient. Statistica Neerlandica, 72(1), 4-13.
Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small
samples and unusual distributions. Sage Publications.
Rao, D. P., & Selvanathan, E. A. (2016). Index numbers: a stochastic approach. Springer.

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Rietveld, T., & van Hout, R. (2017). The paired t test and beyond: Recommendations for
testing the central tendencies of two paired samples in research on speech, language and
hearing pathology. Journal of communication disorders, 69, 44-57.
Wang, J. (2013). Pearson correlation coefficient. Encyclopedia of systems biology, 1671-
1671.