Multiple Linear Regression Analysis 2022

Running Head: Multiple Linear Regression. 1
Application of Multiple Linear Regression to Solve the Big Grocery Management
Problem.
Name
Institution
Date
Professor

Regression Modelling 2
According to Chatterjee and Hadi (2015), the MLR equation can be written as: Y=I0 +
I1X1 + I2X2 + . . .+ InXn + μ where, Y is the dependent variable, I’s are the coefficients, X’s are the
independent variables and μ is the error term.
In the analysis, we need to find the management choice to apply to a new store. This lead
question was affected by three major factors which include; the store size, the location, and the
management. There were 10 locations which were summarized basing on three variables
collected. These outcomes included the revenue, population of customers and the size in square
feet of different business branches. Thus, the idea is to define the dependent and independent
variables (Cox & Roxbee, 2018) and then apply the analysis.
The dependent variable for this analysis was the revenue amount collected from
different locations. The independent variables included: -
 Size – this is the size in square feet of each branch in a different location.
 Population – The number of customers who visit a particular branch
“The good data scientist has thought about these subjective choices and is willing and ready to
answer questions about these decisions.” (Curtis, 2019, p.g.4). To find the relationship that exists
between revenue, size and population, a multiple linear regression becomes the wisest choice.
Sample data for this analysis is shown below (Refer to appendix 1 & 2).
Table 1: Sample Data
Locatio
n Revenue(y)
Size
(sqFt)(x1)
Population(x
2)
Loc1 $23,665,319.22 48720.39 146073
Loc2 $20,066,838.98 40778.72 134878
Loc3 $23,508,691.46 21654.19 225131
Loc4 $11,748,300.32 33344.11 49987
Loc5 $33,450,105.86 116006.4 89939
Loc6 $18,248,754.69 44655.98 53514
Loc7 $10,943,196.86 8549.08 127423
Loc8 $32,934,788.04
157424.4
8 26790
Loc9 $16,821,187.57 63075.32 17092
Loc10 $19,285,241.45 53256.79 86985

Regression Modelling 3
The model equation for this business problem thus can be stipulated by the following
regression equation (James et al., 2013): -
Revenue = I0 + I1(Size) + I2(Population)+ μ.
Results and Interpretation.
The driving force of the question was to find if the size and population, affects the
revenue incurred by Big Grocery. After visualization, the following compound scatter plot
was obtained.
Figure 1: Compound Scatter Plot.
0 50000 100000 150000 200000 250000
$0.00
$50,00,000.00
$1,00,00,000.00
$1,50,00,000.00
$2,00,00,000.00
$2,50,00,000.00
$3,00,00,000.00
$3,50,00,000.00
$4,00,00,000.00
f(x) = 140.31 x + 12824569.32
R² = 0.68
f(x) = 2.49 x + 20828464.07
R² = 0
Compound Scatter Plot
Population Linear (Population)
Linear (Population) Size (sqFt)
Linear (Size (sqFt)) Linear (Size (sqFt))
Size and Population.
Revenue
As clearly depicted, the linear relationship between size and revenue is high compared to
that of Population. This however can be boosted by performing multiple linear regression using
both size and population combined. The assumption will be Revenue depends on both Size and
Population of the grocery store.
With the above model in question, using data analysis tool-pack in excel, the following
output was produced.
Table 2: Regression Statistics.
SUMMARY OUTPUT