Statistical Analysis of Furniture Orders and Mobile Phone Sales

This report delves into the statistical analysis of a furniture order dataset and a mobile phone sales dataset. It utilizes various statistical tools and techniques, including frequency distribution, relative frequency distribution, histograms, ANOVA tables, and regression analysis. The report aims to understand the relationships between variables, analyze the distribution of data, and interpret the results to facilitate informed decision-making.

Statistics HI-6007
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Table of Contents
Introduction..........................................................................................................................................3
Question 1.............................................................................................................................................4
Question 2.............................................................................................................................................6
Question 3.............................................................................................................................................7
Question 4.............................................................................................................................................9
Conclusion...........................................................................................................................................12
References...........................................................................................................................................13
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Introduction
The report consists of various tools of statistical analysis of the data set that is being provided.
There is the inclusion of various techniques such as the frequency distribution, relative frequency
distribution, histogram, ANOVA Table etc. The statistical tools are used to analyze the various
aspect of the different variable for the decision making process. The decision making is being
facilitated by analyzing the factors and variable and relation among them. There are various
questions that are being answered with different statistical tools and techniques to find relativity
between the variables, deviation among different means etc. There is an interpretation of the
answers that are being received with the help of statistical tools and analysis. These tools are
very much useful in the decision making process different levels of management.
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Question 1
The task consists of calculation of the frequency distribution and relative frequency distribution
along with the shape of it on the dataset made on the basis of orders that have been received by
the Missy Walters of furniture.
(a)
Frequency distribution of the value of furniture of orders
Class
Limits
Frequency
distribution
Relative frequency
distribution
Frequency
distribution (%)
123-173 8 0.16 16%
173-223 16 0.32 32%
223-273 11 0.22 22%
273-323 4 0.08 8%
323-373 5 0.1 10%
373-423 2 0.04 4%
423-473 3 0.06 6%
473-523 1 0.02 2%
Total 50 1 100%
The class limits have been made with an interval difference of 50. The Frequency distribution is
done on the basis of the value of furniture lying between the class intervals. The relative
frequency distribution is calculated by dividing the frequency of particular class by the total
number of frequency.
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(b)
1 2 3 4 5 6 7 8
0%
5%
10%
15%
20%
25%
30%
35%
Class Limits
Furniture orders
Histogram showing the percent frequency
distribution of the furniture-order values.
It can be understood with the help of the above histogram that the most of the purchases are
being done in the second class limits which are 173-223 whereas least in the last class interval
being 473-523. The skewness of the histogram is aligned to the left and can be stated that the
most of a number of orders is at the beginning of the class intervals.
(c)
It can be seen that the median will be a suitable tool as a measure of location for the data set
provided. The median will help to differentiate the data set from the middle which is useful in
determining any variation and the frequency of the data in an effective way. The dataset can be
presented in a more appropriate way by parting the frequency from the middle.
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Question 2
ANOVA TABLE
Sources of
Variation
Degree of
freedom
SS MS F
Regression 1 5,048.82 5,048.82 £74.14
Error 46 3,132.66 68.10
Total 47 8,181.48
Sample size 48
Coefficient of
Determination
62%
Coefficients Standard
errors
t Stat
Intercept 80.39 £3.10 £25.92
X 2.14 £0.25 -£8.62
(a)
It can be determined with the help of the analysis that the demand and unit price are related to
each other in a positive way. The F value of the data set and ANOVA table it can be determined
that the F value is much higher in comparison to the current market share price.
(b)
The coefficient of determination is used to determine or predict the variance between the
outcomes of the two variables with this model. It can be interpreted with the coefficient of
determination which is 62% that the reason for the deviation in the outcome achieved can be
understood with the model. The increase in the variable is may result in the increase in the
coefficient of determination even if it is not associated with the outcome.
(c)
The coefficient of correlation is used to determine the relationship between the two variables and
how strong they are. The coefficient of correlation is calculated above through which it can be
determined that there is a positive relationship between the variables demand and the unit price
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of the product. The movement of the variables is in the same direction dependent on each other
that is a change in one variable may affect the other variable making it a positive relation. The
coefficient of correlation calculated with the help of the data set is 2.14.
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Question 3
ANOVA
Source of Variation SS df MS F P-value
Between Groups 390.58 2 195.29 25.89 0.96
Within Groups 158.4 21 7.54
Total 360 23
dfb = k-1
= 3-1
= 2
dfe = n-k
= 24-3
= 21
dft = n-1
23 = n-1
n = 23+1
n = 14
MSB = SSB / dfb
= 390.58 /2
= 195.29
MS (Within) = SS(Within)/ df(between)
= 158.4/21
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= 7.54
F = MSB / MSE
= 195.29 / 7.54
= 25.90
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Question 4
(a)
Coefficients Standard
Error
t Stat
Intercept 0.81 0.00
x1 0.50 0.46 1.08
x2 0.47 0.04 12.23
The regression equation that can be interpreted from the above is
y= 0.8051+0.4977x1 + 0.4733x2
(b)
ANOVA
Degree of freedom SS MS F
Regressio
n
2 40.70 20.35 80.12
Residual 4 1.02 0.25
Total 6 41.72
The P value is = 0.00593
It can be interpreted with the help of the F-test that there is a relationship between the dependent
and the independent variables as the p-value which is obtained is less than 0.05.
(c)
t-value can be can be calculated with the help of the following formula = Coefficient/ Standard
Error.
Carrying out the test:-
For B1
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t = 0.4977/ 0.4617
t = 1.0779
df = n-k-1
= 7-2-1 = 4
P value from the t score is 0.3417 which is greater than 0.05 therefore it can be interpreted that
null hypothesis cannot be rejected and B1 = 0
For B2
t = 0.4733 / 0.0387
= 12.229
P value from the t score is 0.000257 which is lower than 0.05 therefore the null hypothesis can
be rejected and B2 is not equal to 0.
(d)
It can be interpreted that increase in the Unit of X2 there is an increase in the value of B2 being
equal to 0.473.
(e)
Price of phones x1 20
Advertising spot x2 10
Sales revenue of
mobile phones y
15.49
The expected number of mobile phone that can be sold can be calculated with the help of the
following equation
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y= 0.8051+0.4977x1 + 0.4733x2
= 0.8051 + (0.4977 x 20) + (0.4733 x 10)
= 15.492
The numbers of phones that can be sold are 15.492 on an average.
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Conclusion
It can be concluded with the help of the above calculation that the statistical tools can be used to
determine the relationship between different variables. The reason for the outcome can also be
determined with the help of the statistical techniques such as coefficient of correlation and
variance.
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