Regression Analysis for Departmental Store Revenue

Introduction
I work in a departmental store which deals in selling various products. The objective of this
project is to analyse the revenue on the basis of number of items (Quantity), age of customer,
gender of customer, and income of customer.
Methodology
The method of Regression Analysis is used to analyse the revenue of departmental store. The
dependent variable is revenue. The independent variables are number of items (Quantity), age
of customer, gender of customer, and income of customer. The regression model is expected
to be in the form of revenue = bo + b1* Quantity + b2*age + b3*female + b4*income
Data
The data is collected with the help of cluster sampling. All the data regarding the customer
and revenue is collected for the month of January 2019.
The variables revenue, quantity, age and income are measured by the ratio scale of
measurement. The variable gender is measured by the nominal scale of measurement. It is
coded as 1 for female and 0 for male.
Analysis
Consider the null hypothesis, Ho: the regression model is not significant. This is tested
against an alternative hypothesis, h1: the regression model is significant. With F= 0.8419 and
p-value greater than 5%, there is no sufficient evidence to conclude that the regression model
is significant.
Degrees of
Freedom
Sum of
Squares
Mean of
Squares
F p-Value
ANOVA Table
Explained 4
44572.32
588
11143.08
147
0.841944
97 0.4997
Unexplained 244
3229322.
55
13234.92
848

The regression equation is as obtained from the column of coefficients is Revenue =
209.24411914 - 3.18285248 Quantity + 0.56217855 Age - 16.8176802 Female +
0.00000819 Income
With 1 number increase in items bought (quantity), there is 3.18$ decrease in the revenue.
With 1 year increase in the age of the customer, there is $0.56 increase in the revenue. For
female customers, the revenue is 16.8$ less as compared to the male customers.
Coefficient
Standar
d
Error
t-Value p-
Value
Confidence Interval
95%
Multicollinearity
Checking
Regres
sion
Table Lower Upper VIF
R-
Square
Consta
nt
209.244
1191
38.611
97285
5.4191
51203
<
0.00
01
133.18
88037
285.29
94346
Quanti
ty
-
3.18285
2484
2.4929
0818
-
1.2767
62823
0.20
29
-
8.0932
18465
1.7275
13497
1.0048
84506
0.0048
60763
Age
0.56217
8554
0.9780
53114
0.5747
93481
0.56
60
-
1.3643
25911
2.4886
83019
1.0187
82795
0.0184
36506
Femal
e
-
16.8176
802
14.693
89513
-
1.1445
352
0.25
35
-
45.760
74492
12.125
38452
1.0147
2478
0.0145
11107
Incom
e
8.186E-
06
0.0005
14143
0.0159
21645
0.98
73
-
0.0010
04538
0.0010
2091
1.0198
96038
0.0195
07908
Consider the null hypothesis, ho1: the coefficient of quantity is not significant. This is tested
against an alternative hypothesis, h11: the coefficient of quantity is significant. With t= -
1.2767 and p>5%, I fail to reject the null hypothesis and conclude that the coefficient of
quantity is not significant. Chatterjee, S., & Hadi, A. S. (2015).
Consider the null hypothesis, ho2: the coefficient of age is not significant. This is tested
against an alternative hypothesis, h12: the coefficient of age is significant. With t= 0.574 and
p>5%, I fail to reject the null hypothesis and conclude that the coefficient of age is not
significant. Chatterjee, S., & Hadi, A. S. (2015).

Consider the null hypothesis, ho3: the coefficient of female is not significant. This is tested
against an alternative hypothesis, h13: the coefficient of female is significant. With t= -
1.1445 and p>5%, I fail to reject the null hypothesis and conclude that the coefficient of
female is not significant. Chatterjee, S., & Hadi, A. S. (2015).
Consider the null hypothesis, ho3: the coefficient of income is not significant. This is tested
against an alternative hypothesis, h13: the coefficient of income is significant. With t=
0.0159 and p>5%, I fail to reject the null hypothesis and conclude that the coefficient of
income is not significant. Chatterjee, S., & Hadi, A. S. (2015).
Multiple Regression for
Revenue Multip
le
R
R-
Squar
e
Adjust
ed
R-
squar
e
Std. Err. of
Estimate
Summary
0.11
67
0.01
36
0.00
00
115.0431
592
The coefficient of determination is 1.3% only. There is only 1.3% variation in the revenue
which is explained by quantity, age, female and income. This percentage is very less and the
fitted model is said to be a bad fit for the data. Schroeder, L. D., Sjoquist, D. L., & Stephan,
P. E. (2016).
Multi-co-linearity is an undesirable situation where independent variables are correlated with
each other. With VIF < 10, there is no problem of multi-co-linearity in the data. The same is
also evident from the Correlation Matrix. Fox, J. (2015).
Correlation Matrix Revenue Quantity Age Female Income
Revenue 1.000 -0.080 0.038 -0.077 0.000
Quantity -0.080 1.000 0.048 0.012 0.042
Age 0.038 0.048 1.000 -0.075 -0.093
Female -0.077 0.012 -0.075 1.000 -0.085
Income 0.000 0.042 -0.093 -0.085 1.000
To test the assumption of normality of the regression model, the histogram of the residual is
given below.