Statistics for Business: Comprehensive Analysis of Statistical Methods

This report provides a comprehensive analysis of statistical methods relevant to business applications. It begins with an introduction to statistics and then delves into the construction and interpretation of frequency distributions, including cumulative, relative, and percentage frequency distributions, illustrated with a histogram chart. The report then explores regression analysis, calculating sample size, determining the significance of relationships between variables like demand and unit price, and computing the coefficient of correlation. Furthermore, it examines the relationship between supply and unit price, predicts supply based on price, and constructs and interprets an ANOVA table to advise a company on productivity programs. The report also includes the development of a regression equation to analyze the relationship between weekly sales and product price, and the determination of the slope coefficient. The analysis utilizes statistical tools to draw conclusions and provide insights into the data.

Statistics for Business

Table of Contents
INTRODUCTION...........................................................................................................................1
QUESTION 1...................................................................................................................................1
(a): Construction of frequency distribution............................................................................1
(b): Histogram chart...............................................................................................................2
QUESTION 2...................................................................................................................................2
(a): Calculation of sample size...............................................................................................2
(b): Determine effect or not demand and units price relations...............................................3
(c): Compute the coefficient of correlation and relationship..................................................3
(d): Relationship among supply and unit price.......................................................................3
(e): Predict the supply (in units).............................................................................................3
QUESTION 3...................................................................................................................................4
(a): Calculation of ANOVA table...........................................................................................4
(b): Advise to the Allied........................................................................................................4
QUESTION 4:.................................................................................................................................5
(a): Regression equation.........................................................................................................5
(b): Determine the model is significant..................................................................................5
(c): Relation among sales, price and advertising....................................................................6
(d): Re-estimate the model.....................................................................................................6
(e): Slope coefficient..............................................................................................................6
CONCLUSION................................................................................................................................7
REFERENCES................................................................................................................................8

INTRODUCTION
Statistic is a form of mathematical calculation that related with different numerical data
in large quantities. It deals with all aspects of data that include planning, collection of data in
term of surveys and experiments. Under this report, various statistic method has been used to
understand the importance of statistic such as calculation of frequencies and cumulative
frequency calculation. The other question based on regression analysis associated with the
supply and unit price of the variables. Construction of ANOVA table and statistical consultant to
allied to advise them effectively at 0.5 level of significance difference. Apart from this, use of
excel regression tool to answer the various question are done accordingly under this report.
QUESTION 1
(a): Construction of frequency distribution
Frequency distribution: In statistics, a frequency distribution is considered as one of the
effective list, table or graph that would displays overall class of various marks scored by the
student.
Cumulative frequency distribution: It is an effective analysis of the frequency arises of
values is a phenomenon less than a reference value. in order to find the relative frequency, divide
the frequency through the total number of data values.
Relative frequency distribution: It used to indicate total number of elements in a given
data set that belong to each class. In case of relative frequency, the value is assigned to each class
in the proportion of total data set that is associated with the class.
Percentage frequency distribution: To calculated this particular value, simply divide
the frequency by total number of outcomes and multiply it with 100.
Examination
score Frequency
Cumulative
freq.
Relative
freq.
Com. Relate.
Freq
%
frequency
51-60 3 3 0.15 0.15 15
61-70 2 5 0.1 0.25 10
71-80 6 11 0.3 0.55 30
81-90 4 15 0.2 0.75 20
91-100 5 20 0.25 1 25
Total 20
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(b): Histogram chart
From the above chart, it has showing percentage frequency distribution which is
indication the proportion of all the observation of the mentioned class intervals. Instead of the
counts, this report is providing frequencies percentage of the marks scored by the 20 students. It
used to display essential data that specifies the observation percentage that exist for each data
point or grouping of points. It is basically crucial methods of expressing the relative frequency of
survey responses and other data. The shape of histogram is indicating a skewed distribution to
the right as shown in the above. After analysing the score, it shows that the most data is skewed
towards the left which would indicate that, most of the students appeared in examination attain
more than 71 or close to it. While, less than 71 score has minimum percentage of frequency. It
means that the overall data is stretched towards the upper score values.
QUESTION 2
(a): Calculation of sample size
Below mentions formula for the calculation of sample.
DF=n-1
In which,
The DF that denotes the degree of freedom.
The “n” indicates the overall size of the sample.
Now, sample can be calculated by following process.
N=DF+1
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After deducting of the value of the DF.
N=40+1
N=41.
Thus, the overall sample size for this particular test was 41, as analysis used to perform above.
(b): Determine effect or not demand and units price relations
This particular analysis is done in accordance with the earlier section that guide credible
matters regarding the significance level of overall relationships among the supply units and unit
price. It would examine its value to be 0.087. This results can have collected after using T-score
the outcome of the analysis indicate the current relationship among the supply and unit price
which is not significant at the given confidence level of 0.05. The p-value is higher than 0.05.
(c): Compute the coefficient of correlation and relationship
R2=SSR/SST
R2=354.689/7035.262
= 0.0504(5.04%)
From the above calculation, it has been found that there is coefficient determination of
0.0504 which would indicate that overall sample for this model is capable of covering an
approximate value of 5.04% variable. It is basically taken into account for the purpose of
measuring the strength of a liner association among two variables.
(d): Relationship among supply and unit price
The ‘R’ indicate that the square root of R²
Therefore,
R =
R = 0.224
According to the above calculation, it has been found that there is positive correlation
among the supply and unit prices as they value is 0.224.
(e): Predict the supply (in units)
Let's take supply as 'Y' then, the equation will be Y = 54.076 + 0.029 (X)
From the above equation of regression:
Y= Supply of units
X= Price of units
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After deducting the value of the X in the above mentioned equation
Y = 54.076 + 0.029 (50000)
Y = 54.076 + 1450
Hence:
Y = 1504.076
QUESTION 3
(a): Calculation of ANOVA table
Anova: Single
Factor
SUMMARY
Groups Count Sum Average Variance
Program A 5 725 145 525
Program B 5 675 135 425
Program C 5 950 190 312.5
Program D 5 750 150 637.5
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 8750 3 2916.666667 6.140350877 0.00556986 3.23887152
Within Groups 7600 16 475
Total 16350 19
From the above mentioned ANVO was taken into account to test the following hypothesis:
H0: μ1 = μ2 = μ3 = μ4
H1: One or more means are different.
As per the nature of the case, Null hypothesis will be rejected in case the value of F is maximum
than the value of F. The calculation show F is 6.14 which is higher than the value that is 3.238.
(b): Advise to the Allied
In order to increase the productivity of their line workers, all the four various programs
have been suggested to assist productivity of the company. After making ANOVA table, it has
been found below mentioned hypothesis. Eventually rejecting the null hypothesis H0: μ1 = μ2 =
μ3 = μ4. Thus, this is clearer that all four events do not produce equal amount of productivity.
According to the outcome that used to produce another analysis, average productivity of 145,
135, 190 and 150 is effective manner.
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QUESTION 4:
(a): Regression equation
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.87
7814
35
R Square
0.77
0558
04
Adjusted R
Square
0.65
5837
06
Standard
Error
1.83
7409
75
Observations 7
ANOVA
df SS MS F
Significance
F
Regression 2
45.3528
445
22.67
64222
6.71680
13 0.052643614
Residual 4
13.50
42984
3.376
0746
Total 6
58.8571
429
Coe
fficie
nts
Standar
d Error t Stat P-value Lower 95% Upper 95% Lower
90.0%
Upper
90.0%
Intercept
3.59
762 4.05224
0.887
81 0.42481 -7.6532 14.8484 -
5.0411 12.2364
Price
41.3
2 13.3374
3.098
07 0.03629 4.28957 78.3505 12.886
8 69.7532
Advertising
0.01
324 0.32759
0.040
42 0.96969 -0.8963 0.92278 -
0.6851 0.71162
Y = 3.598 + 41.32 (X1) + 0.0132 (X2)
(b): Determine the model is significant
From the above regression analysis, it has been found that hypothesis test assist researcher
to decide the value of overall sales. Use of regression line to model the linear relationship among
x and y. The rules say that in case the p-value is less than the significance level of (α=0.10) the
null hypothesis is rejected. There is sufficient evidence to conclude that there is an effective
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significant linear relationship among x and y because the correlation coefficient is significantly
different from Zero. A thorough analysis of this model has been examine certain value such as F-
values and significance level of the model that are 6.7168013 and 10.052.
(c): Relation among sales, price and advertising
In order to taken into the independent variables, the price of items produced by competitors
has confidence values of 0.1 that is higher than their significance level that is 0.036 which
depicts the availability of statistically significant relationships. It taken into account the weekly
and price of products produced by the competitors.
(d): Re-estimate the model
Regression Statistics
Multiple R 0.877760967
R Square 0.770464315
Adjusted R Square 0.724557178
Standard Error 1.643764862
Observations 7
ANOVA
df SS MS F
Significance
F
Regression 1 45.34732824 45.34732824 16.7831053 0.009384894
Residual 5 13.50981461 2.701962923
Total 6 58.85714286
Coefficient
s
Standard
Error t Stat P-value
Lower
95%
Uppe
r 95%
Lower
90.0%
Uppe
r
90.0%
Intercept 3.58 3.61 0.99 0.37 (5.69) 12.86 (3.69) 10.85
Price 41.60 10.16 4.10 0.01 15.50 67.71 21.14 62.07
Below mentioned the regression equation that has been re-estimated in perspective of
above model as shown below:
Y = 3.58 + 41.60 (X1)
Y= Weekly sales
X1= unit of products price.
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(e): Slope coefficient
As discussed in the earlier section, the following regression equation can be taken into
account to examine the overall nature of relationship among certain variables such as weekly
sales and price of products. Y = 3.58 + 41.60 (X1).
For this case, the value of coefficient is 41.40 which would indicate that overall increase of
units in cost of products that are produced by the company market competitors. It can lead to
enhance the 41.60 units from their weekly sales.
CONCLUSION
From the above report, it is clearly concluded that statistics is useful in doing calculation
on large number of data. In above report, statistic calculation is used to determine overall
cumulative frequency for a particular class, it make easy for the calculation of regression
analysis and is useful in determining price of overall project.
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REFERENCES
Books and Journal:
Chatfield, C., 2018. Statistics for technology: a course in applied statistics. Routledge.
Fearnhead, P. and Prangle, D., 2012. Constructing summary statistics for approximate Bayesian
computation: semi‐automatic approximate Bayesian computation. Journal of the Royal
Statistical Society: Series B (Statistical Methodology). 74(3). pp.419-474.
Moorthy, A. K. and Bovik, A. C., 2011. Blind image quality assessment: From natural scene
statistics to perceptual quality. IEEE transactions on Image Processing. 20(12). pp.3350-
3364.
Schervish, M. J., 2012. Theory of statistics. Springer Science & Business Media.
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