Statistical Data Analysis: Interpretation and Application Report

This assignment provides a comprehensive analysis of statistical data, starting with the creation and interpretation of a histogram based on a given dataset, focusing on identifying key order categories for business improvement. It then delves into Analysis of Variance (ANOVA) and regression analysis, interpreting F and p-values to determine the significance of the relationship between demand and price, and assessing the model's fit using the coefficient of determination. Further, the assignment examines variations between treatments and computes regression values to model sales of mobile phones based on price and advertising spots, ultimately demonstrating how changes in advertising positively impact sales. Desklib is a valuable resource for students seeking solved assignments and study materials.

Table of Contents
Part 1...........................................................................................................................................................2
Part 2...........................................................................................................................................................3
Part 3...........................................................................................................................................................5
Part 4...........................................................................................................................................................5
References...................................................................................................................................................6

Part 1
The 1st question is focused in stating the class interval of the data set which is given in the
question, the student need to prepare in detail the histogram of the data based on the seggregation
in bins, the bin set is stated as
Bin
data set
50
100
150
200
250
300
350
400
450
500
Class
interva
l
Frequenc
y of the
data set
Overall in
%
Cummu in
% terms
0 – 50
values 0 0.00% 0.00%
50 –
100
values 0 0.00% 0.00%
100 –
150
values 3 6.00% 6.00%
150 –
200
values 15 30.00% 36.00%
200 –
250
values 14 28.00% 64.00%
250 –
300
values 6 12.00% 76.00%
300 –
350
4 8.00% 84.00%

values
350 –
400
values 3 6.00% 90.00%
400 –
450
values 3 6.00% 96.00%
450 –
500
values 2 4.00% 100.00%
Total
Sum 50 100.00% 100.00%
Charting pattern of Histogram
0 -
50 50 -
100 100
-
150
150
-
200
200
-
250
250
-
300
300
-
350
350
-
400
400
-
450
450
-
500
0
2
4
6
8
10
12
14
16
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Histogram
Frequency
Cumulative %
Bin
Frequency
Measure of location
From the analysis it is noted that the management of the company need to focus on three major
catgories of the orders which are classified as 150 values, 200 values and 250 values, because
these 3 categories nearly account to more than 60% of the sales of the company and it is noted
that more customers are purchasing the goods. This will enable in enhancing the revenues, attract
more customers and generate large profits to the company.
Part 2

The 2nd question deals in preparing exhaustive analysis based on the data given in the Analysis of
Variance table and the regression output table.
Degr.
Of
freed.
Sum of
the
squares
of value
M. of
square
values
Value of
F
F –
significanc
e value at
5%
Regre. 1
5,048.8
2
5,048.8
2 74.14 0.0
Residual 46
3,132.6
6 68.10
Total 47
8,181.4
8
The value of M square = Sum of the square value / Deg of freedo
Value of the F = M squre regression / Residual
Regression table
Value
of the
Coeff
Error –
Standar
d
Statistic
– t value
Value
of P
(0.05)
Intrcepts 80.3 3.10 25.89 0.00
X value -2.14 0.25 -8.62 0.00
Statistic – t value is computed by value of the coeff / error
From the overall analysis of ANOVA and Regression it is noted that the f value and p value is
computed to be 0.00, this shows that there is a significant association betwee demand and the
price.
Coefficient of determination
The value of the coefficient of determination is intended to understand the best fit for the model
based on the data, it is usually denoted as R squared. The value if it is excess of more than 0.6,
then it can be stated that the model is considered to be the best fit.
The value of coeff. Of determ is
Value of R squared = 1 – Residual value of sum square / total sum square

= 1 - 3132.66 / 8181.48
= 62%
Based on the analysis the coefficient of determination is 62% showing that the model is a best fit
and the aspects stated that the variability in the independent variable is stated through the
variability of the dependet variable
The coefficient of correlation
This shows the association between two variables and it usually lies between -1 to + 1, this is
computed as
R multiple value = SQRT of the value of R squ
= 0.79,
The value of the slope stated in the problem is negative , therefore the correlation is -0.79
showing a negative correlation between the variables.
Therefore it can be concluded that the increase in the price of the product will decrease the
demand of the products
Part 3
Variations Su of Squar Degr. Of free. M Square
Value
the F
Significanc
e for F
(0.05)
Bet. Treatments 390.58 3 130.19 16.44 0.000
Error aspects 158.4 20 7.9
Sum 548.98 23
It is noted that the degree of freedom for the between the treatments is 3 and the total is 23, so
the error aspects is 20. Moreover, the mean square value is stated as
130.19 / 7.9 = 16.44
The mean value of the square shows that there is a overall relationship between the variable
(Triola, 2014)
Part 4

This part intends to compute the regression values based on the equation
Y (Sales of the mobile phones) = Cons + X1 (Price of the phone) + X2 (Advertising spots of the
phone)
Y (Sales of the mobile phones) = 0.81 + 0.4977 x Price of the phone + 0.4733 x Advertising
spots of the phone
Degr. Of
free
Sum of the
squares
M of the
squares
Value of
the F
Sgnifican
c
Regr value 1 40.7 40.7 240.35 0
Resi value 6 1.016
0.16933333
3
From the analysis it shows that there is a relationship between the sales of the phones and the
price & adv spots. The value of the coeffic of spots is 0.477, this stats that the changes in the ad
spots will postively impact the sale of the phones.
Price = 20, spots = 10
Y (Sales of the mobile phones) = 0.81 + 0.4977 x Price of the phone + 0.4733 x Advertising
spots of the phone
= 0.81 + 0.4977 x 20 + 0.4733 x 10
= 15 phones
References
1. Freedman, David (2010). Statistics. 4th Edition. Cengage Publishing
2. Sarah Boslaugh (2012). Statistics in a Nutshell. Cengage Publishing
3. Triola (2014). Essentials of Statistics. 5th Edition. McGraw Hill