Statistics for Business Decision

This report focuses on statistics for business decision making and regression analysis. It covers topics such as assessing mean, median, mode, range, variance, and standard deviation for each business type, testing significant differences in starting costs, estimating regression equation, and evaluating model fit. The report provides insights into using statistical tools for effective decision making in business.

Statistics for Business Decision

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
TASK 1............................................................................................................................................1
1. Assessing mean, median, mode, range, variance and standard deviation for each business...1
2...................................................................................................................................................2
a. Stating frequency and relative distribution for each business type construct..........................2
b. Presenting a relative frequency histogram...............................................................................2
3. Discussing results....................................................................................................................2
4. Testing significant differences in the starting cost of each type of business...........................3
TASK 2............................................................................................................................................6
1. Presenting output with the estimated regression equation.......................................................6
2. Stating the extent to which model fits to the data....................................................................7
3. Testing hypothesis by considering both dependent and independent variables......................8
4. Interpreting individual slope coefficients................................................................................9
5. Constructing 95% confidence interval for the slope coefficient of individual variables........9
6. Testing estimated slope coefficients........................................................................................9
7. Re-estimation of model by removing all insignificant variables.............................................9
8. Predicting annual sales for franchisee...................................................................................11
CONCLUSION..............................................................................................................................11
REFERENCES..............................................................................................................................12

INTRODUCTION
In the present era, business units lay high level of emphasis on using statistical tools for
effectual decision making. Moreover, statistical tools and techniques help in summarizing the
large data set and thereby give input for the development of competent as well as strategic
framework. The present report is based on different case situations which will provide deeper
insight about the manner in which regression and T test helps in finding significant differences
between the assessed variables. It will also shed light on the ways through which analyst can
assess insignificant variable and re-estimate the effectual one.
TASK 1
1. Assessing mean, median, mode, range, variance and standard deviation for each business
Descriptive statistics of the start-up cost pertaining to the different types of business such as
pizza (X1), baker (X2), shoe stores (X3), gift shops (X4)) and pet stores (X5) are as follows:
Particular
s X1 X2 X3 X4 X5
Mean 83
92.090
9 72.3 87 51.625
Standard
Error
9.4672
2
11.726
8
9.9186
1
11.353
9
6.7687
2
Median 80 87 70 97.5 49
Mode 35 #N/A #N/A 100 30
Standard
Deviation
34.134
5
38.893
3
31.365
4
35.904
2
27.074
9
Sample
Variance
1165.1
7
1512.6
9
983.78
9
1289.1
1 733.05
Range 105 120 90 115 90
Count 13 11 10 10 16

2.
a. Stating frequency and relative distribution for each business type construct
Frequency table and relative distribution is enumerated below:
Class
/
Busin
ess
type
Piz
za
(X
1)
Relativ
e
distribu
tion
Bak
er
(X2
)
Relative
distribu
tion
sh
oe
sto
re
(X
3)
Relativ
e
distribu
tion
Gi
ft
sh
op
(X
4)
Relative
distribu
tion
Pet
stor
es
(X5
) Relative
distribution
0-30 6 0.38
31-60 4 0.31 3 0.27 4 0.40 3 0.3 5 0.31
61-90 4 0.31 4 0.36 3 0.30 1 0.1 4 0.25
91-
120
3 0.23 2 0.18 2 0.20 5 0.5 1
0.06
121-
150
2 0.15 1 0.09 1 0.10 1 0.1
0.00
151-
180
0.00 1 0.09 0.00 0
0.00
Total 13 1 11 1 10 1 10 1 16 1
b. Presenting a relative frequency histogram
0.25 More 0
0
2
4
6
8
10
12
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Histogram
Frequency
Cumulative %
Bin
Frequency
3. Discussing results
Interpretation of descriptive statistics: By doing analysis it has found that average start
up cost of pizza, baker shop and gift shops account for $83, $92.09 & $87 respectively. On the
other side, out of 5 variables assessed mean start-up cost of pet-stores is highly lower. Further,
outcome of descriptive statistics show that 50% respondents invested approximately $97.5 for

starting the business of gifs item. Hence, by considering the median values of all the variables
from X1 to X5 it can be stated that higher investment is required in the business of gift shop. In
contrast to this, business pet store fall into the category of one which demands for lower
investment. Along with this, value of standard deviation shows that in the near future mean start-
up cost of businesses (X1 to X4) will deviate within the range of 31 to 38. Hence, by keeping all
such aspects in mind it can be presented that business entity with lower funds can start pet stores
over others and thereby would become able to attain higher margin. By doing analysis, it has
been assessed that relative frequency in the context of pet store is.38 when class is between 0-30.
In addition to this, relative distribution is .31 when class is 31-60 & 61-90.
4. Testing significant differences in the starting cost of each type of business
Summary statistics
Variable
Observation
s
Obs.
with
missin
g data
Obs.
witho
ut
missin
g data
Minimu
m
Maximu
m Mean
Std.
deviatio
n
X1 10 0 10 35.000 140.000
83.90
0 33.825
X2 10 0 10 40.000 160.000
92.30
0 40.991
X3 10 0 10 35.000 125.000
72.30
0 31.365
X4 10 0 10 35.000 150.000
87.00
0 35.904
X5 10 0 10 20.000 80.000
39.10
0 21.794
X1 (pizza): 95% confidence interval on the difference between means account for 59.70 &
108.97
t (Observed value) 83.900
t (Observed value) 7.844

|t| (Critical value) 2.262
DF 9
p-value (Two-tailed) < 0.0001
alpha 0.05
X2 (baker): @ 95% confidence interval difference between means is 62.98 & 121.62
Difference 92.300
t (Observed value) 7.121
|t| (Critical value) 2.262
DF 9
p-value (Two-tailed) < 0.0001
alpha 0.05
X3 (shoe stores): On 95% confidence interval difference between the mean values is 49.86 &
94.74 respectively
Difference 72.300
t (Observed value) 7.289
|t| (Critical value) 2.262
DF 9
p-value (Two-tailed) < 0.0001
alpha 0.05
X4 (gift shops): Difference between means @ 95% confidence interval implies for 61.32 &
112.68
Difference 87
t (Observed value) 7.663
|t| (Critical value) 2.262
DF 9
p-value (Two-tailed) < 0.0001
alpha 0.05

X5 (Pet stores): 95% confidence interval on the difference between means account for 23.51 &
54.69
Difference 39.100
t (Observed value) 5.673
|t| (Critical value) 2.262
DF 9
p-value (Two-tailed) 0.000
alpha 0.05
Summary of p values
Variable p-values
X1 < 0.0001
X2 < 0.0001
X3 < 0.0001
X4 < 0.0001
X5 0.000

X1 X2 X3 X4 X5
0.0E+00
5.0E-05
1.0E-04
1.5E-04
2.0E-04
2.5E-04
3.0E-04
3.5E-04
p-values (Student's t test)
Variable
Interpretation: Summary table of P value clearly shows that there is no statistical
difference takes place in the mean start –up cost of pizza, shoe store, baker and gift shop except
pet store. Thus, on the basis of the outcome of independent sample t test it can be stated that
average investment or start-up cost of pet store business differs over others.
TASK 2
1. Presenting output with the estimated regression equation
 Annual sales (X1)
 Floor area (X2)
 Inventory (X3),
 Advertising expenses (X4),
 Size of business operations (X5)
 Number of competitors (X6)

Hypothesis
H0 (null hypothesis): There is no significant difference takes place in the mean value of sales
and other variables from X1 to X6.
H1 (Alternative hypothesis): There is a significant difference takes place in the mean value of
sales and other variables from X1 to X6.
Summary output
Regression Statistics
Multiple R 0.99658
R Square 0.99318
Adjusted R
Square 0.99156
Standard Error 17.6492
Observations 27
ANOVA
df SS MS F
Significanc
e F
Regression 5
95253
9
19050
8
611.5
9
5.39731E-
22
Residual 21
6541.4
1
311.4
96
Total 26
95908
0
Coefficie
nts
Standa
rd
Error t Stat
P-
value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -18.8594
30.150
2
-
0.625
5
0.538
37
-
81.560245
31
43.84
14 -81.56
43.84
14
X2 16.2016
3.5444
4
4.570
99
0.000
17
8.8305126
96
23.57
26
8.830
51
23.57
26
X3 0.17464
0.0576
1
3.031
54
0.006
35
0.0548367
79
0.294
43
0.054
84
0.294
43
X4 11.5263 2.5321
4.552
05
0.000
17
6.2604719
72
16.79
21
6.260
47
16.79
21
X5 13.5803
1.7704
6
7.670
51
1.6E-
07
9.8984468
36
17.26
22
9.898
45
17.26
22
X6 -5.31097 1.7054 - 0.005 - - - -

3
3.114
2 25
8.8576000
4
1.764
3
8.857
6
1.764
3
Interpretation: Tabular presentation shows that p value < 0.05 in X2, X3 & X4 which
means mean value of sales, floor area, inventory and expenditure varies to the significant. In
accordance with such aspect, all such three variables have significant impact on the annual sales
of Green Pty Ltd’s franchisee. On the contrary to this, when sales is compared with size of area
and competitors then significance value is greater than 0.05. Thus, it can be mentioned that
statistical difference takes place in the mean value of sales, area, inventory and promotional
expenses over others.
Regression equation: y= -39.54 + 16.20 * X2 + .17 * X3 + 11.53 * X4 + 13.58 * X5 + -5.31 *
X6
2. Stating the extent to which model fits to the data
Table of regression statistics depicted above clearly shows that value of r square is .993
respectively. As per the standards, r square is greater than the average limit such as .60 (Brace,
Snelgar and Kemp, 2016). By keeping all such aspects in mind it can be depicted model fits to
the data set to a great extent.
3. Testing hypothesis by considering both dependent and independent variables
For testing hypothesis two variables are considered such as sales and advertisement. The
rationale behind this, promotional activities helps in raising awareness among the customers and
thereby enhances sales revenue. By considering this, variables are categorized in the following
manner:
 Sales: dependent variable
 Promotional or advertising expenses: independent variable
H0 (null hypothesis): There is no significant difference takes place in the mean value of sales
and advertisement expenses.
H1 (Alternative hypothesis): There is a significant difference takes place in the mean value of
sales and advertisement expenses.

Summary output
Regression Statistics
Multiple R 0.91402
R Square 0.83544
Adjusted R
Square 0.82886
Standard Error 79.4547
Observations 27
ANOVA
df SS MS F
Significanc
e F
Regression 1 801254
80125
4 126.92 2.7E-11
Residual 25 157826
6313.0
5
Total 26 959080
Coefficient
s
Standar
d Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -90.15 36.7696
-
2.4517
0.0215
5 -165.88
-
14.421
-
165.88
-
14.421
X4 46.5091 4.12831
11.265
9
2.7E-
11 38.0067
55.011
5
38.006
7
55.011
5
4. Interpreting individual slope coefficients
ANOVA table depicted above presents that slope co-efficient is 46.51 respectively. This
in turn presents that advertising expenses have an impact on firm’s sales but not with a higher
rate (Janssen and Laatz, 2017). Moreover, along with the promotional expenditures there are
several other factors that have high level of influence on the sales revenue of Greens Pty ltd
namely floor area, inventory etc.
5. Constructing 95% confidence interval for the slope coefficient of individual variables
Results generated through regression analysis clearly shows that @ 95% confidence level
lower and upper value implies for $38 & 55 (in’000) respectively. Thus, manager of the firm
should consider such value when developing policies for the near future.

6. Testing estimated slope coefficients
By referring table 4 it can be entailed that value of R and r square implies for .91 & .83
respectively. Further, ANOVA table presents that significance value is higher than the standard
value such as 0.05. In accordance with such aspect, null hypothesis is true due to the movement
of average sales and advertising expenses in similar direction (Frost, 2013).
7. Re-estimation of model by removing all insignificant variables
Correlation assessment
Particulars X1 X2 X3 X4 X5 X6
X1 1 0.89 0.95 0.91 0.95 -0.91
X2 0.89 1 0.84 0.75 0.84 -0.77
X3 0.95 0.84 1 0.91 0.86 -0.81
X4 0.91 0.75 0.91 1 0.80 -0.84
X5 0.95 0.84 0.86 0.80 1 -0.87
X6 -0.91 -0.77 -0.81 -0.84 -0.87 1
Summary output
Regression Statistics
Multiple R 0.995
R Square 0.99003
Adjusted R
Square 0.98822
Standard Error 20.8483
Observations 27
ANOVA
df SS MS F
Significa
nce F
Regression 4
94951
8
237379.51
45
546.1
4 1.2E-21
Residual 22
9562.2
9
434.64972
46
Total 26
95908
0
Coefficie Standa t Stat P- Lower Uppe Lowe Uppe

nts
rd
Error value 95% r 95%
r
95.0
%
r
95.0
%
Intercept -109.17
9.7460
1
-
11.201321
17
1.5E-
10 -129.38
-
88.95
6
-
129.3
8
-
88.95
6
X2 17.4271 4.161
4.1881929
96
0.000
38 8.79768
26.05
65
8.797
68
26.05
65
X3 0.13065
0.0659
7
1.9804186
84
0.060
3 -0.0062
0.267
46
-
0.006
2
0.267
46
X4 15.5146
2.5802
7
6.0127672
04
4.7E-
06 10.1634
20.86
57
10.16
34
20.86
57
X5 16.6611
1.7344
1
9.6062067
45
2.5E-
09 13.0642
20.25
8
13.06
42
20.25
8
Interpretation: For assessing insignificant variable correlation analysis is conducted to
deter mine the extent to which different variables have association with each other. In this,
negative correlation has been found for the variable of competitor. This aspect clearly exhibits
that variable such as competitor is insignificant. By removing such variable regression analysis is
conducted by analyst again and identified that value of r square accounts for .990. On the basis
of such aspect it can be presented that removal of competitor factor from the variable list does
not have significant impact on the value of r square. Thus, business entity or manager of Green
Pty Ltd should focus on the factors such as floor area, inventory, advertising expenses and size of
operations while developing strategies as well as policy framework.
8. Predicting annual sales for franchisee
Computation of annual sales:
VAR X Beta X * beta value
Area 1000 17.43 17427.07
Inventory 150000 0.13 19597.30
Advertisement 5000 15.51 77572.80
Area of operation 5000 16.66 83305.48
Competitors 2 -5.31 -10.62
Total of X* beta value 197892.03
Intercept value -109.2
Annual sales (Total of X * beta + 197782.86

intercept)
Interpretation: The above mentioned table presents that value of sales will be $197782.6
respectively. In this, to derive suitable outcome re-estimated model has been used. Thus,
manager of Greens Pty ltd should develop competent strategies to attain such estimated revenue.
CONCLUSION
From the above report, it has been concluded pet store can be started by the entrepreneurs
with lower funds. Besides this, it can be inferred that manager of Greens Pty Ltd needs to lay
emphasis on improving the aspects of floor area, inventory and size of business. Along with this,
company should focus on both traditional and modern promotional aspects. By doing this, Green
Pty Ltd can enhance sales and would become able to make contribution in the organizational
success.

REFERENCES
Books and Journals
Brace, N., Snelgar, R. and Kemp, R., 2016. SPSS for Psychologists: And Everybody Else.
Palgrave Macmillan.
Janssen, J. and Laatz, W., 2017. Schneller Einstieg in SPSS. In Statistische Datenanalyse mit
SPSS (pp. 5-51). Springer Berlin Heidelberg.
Online
Frost, J., 2013. [Online]. Regression Analysis: How Do I Interpret R-squared and Assess the
Goodness-of-Fit?. Available through: <
http://blog.minitab.com/blog/adventures-in-statistics-2/regression-analysis-how-do-i-interpret-r-
squared-and-assess-the-goodness-of-fit>. [Accessed on 25th September 2017].