Brand Awareness via Online Media: An Evidence Using Instagram Medium with Statistical Analysis

Abstract

Online marketing refers to the practices of promoting a company’s brand to its potential customers. It helps the companies to find new venues and trade worldwide. Numerous online media such as Facebook, YouTube, Twitter, and Instagram are available for marketing to promote and sell a company’s product. However, in this study, we use Instagram as a marketing medium to see its impact on sales. To carry out the computational process, the approach of linear regression modeling is adopted. Certain statistical tests are implemented to check the significance of Instagram as a marketing tool. Furthermore, a new statistical model, namely a new generalized inverse Weibull distribution, is introduced. This model is obtained using the inverse Weibull model with the new generalized family approach. Certain mathematical properties of the new generalized inverse Weibull model such as moments, order statistics, and incomplete moments are derived. A complete mathematical treatment of the heavy-tailed characteristics of the new generalized inverse Weibull distribution is also provided. Different estimation methods are discussed to obtain the estimators of the new model. Finally, the applicability of the new generalized inverse Weibull model is established via analyzing Instagram advertising data. The comparison of the new distribution is made with two other models. Based on seven analytical tools, it is observed that the new distribution is a better model to deal with data in the business, finance, and management sectors.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Advertising means a way of business communication between the company/business firm and its present and prospective audience. It provides information about the business firms, their brand qualities, price, place of availability, etc. For a better business deal, advertisement is essential for both the company and the customers. However, it is more fruitful for the company to reach maximum customers [1].

Advertising is an effective and useful step of marketing to promote a specific brand. Marketing is a collection of the process that involves designing the brand, creation, research, and investigation about how to promote the products/services to the potential and target and customers [2]. An effective marketing program, also known as a marketing plan or marketing strategy, helps to define the price and quality of the product. Several methods have been suggested for marketing a company’s brand. However, marketing through online media is very fruitful to reach the maximum audience [3].

Numerous online platforms such as YouTube, Instagram, Facebook, Pinterest, Twitter, and Flickr are available for online marketing; see Dwivedi et al. (2015). Among the available online platforms for marketing, Instagram is one of the most beneficial tools for online marketing [4].

A decade ago, Instagram was founded by Michel Kriger (a software engineer) and Kevin Systrom (a former Google employee). In April 2012, Facebook bought Instagram for $1 billion. It is one of the most influential and biggest social media platforms (SMPs). In June 2018, this platform had hit one thousand million monthly active users [5]. Due to a large number of active users, it is a very useful platform for online marketing; see Salleh et al. [6] and Yu et al. [7].

In this work, we test the significance of online media on the sales of certain products. For this activity, we choose the Instagram medium among the well-known online platforms. We use a simple linear regression (SLR) model to check the significance of the Instagram medium. Two well-known statistical tests such as the (i) t-test and (ii) F-test, along with the correlation test (CT) are considered to perform the regression analysis (RA).

In addition to the RA, a new flexible statistical distribution (SD) is introduced to model the Instagram sales data. The proposed SD may be called a new generalized inverse Weibull (NIG-Weibull) model. The NGI-Weibull is very flexible and offers a close fit to Instagram sales data.

2. Regression Analysis

Within this section, we provide the RA to see the impact and usefulness of advertising on sales using the Instagram medium. Furthermore, we apply the t-test statistic and F-test statistic to test a hypothesis about the significant role of Instagram advertising in the business sector.

2.1. Simple Linear Regression Model

The SLR model to describe the relationship between Instagram advertising and sales has the following form:$$\begin{array}{}\text{(1)}& Y={\lambda }_0+{\lambda }_1\text{\hspace{0.17em}Instagram\hspace{0.17em}}+\epsilon .\end{array}$$

By implementing the RA technique, we observe that ${\lambda }_0=5.1030$, interpreted as the expected dollar sales (in 1000 s). So, for allocating no advertising budget on Instagram, the expected sale is $5.1030\ast 1000=5103$. The slope of the regression model (regression coefficient) presented in equation (1) is 0.193 5, indicating an increment of 193 (0.193 5 $\ast$ 1000) units in the sales. This fact shows that by spending money on Instagram medium, the expected sale is 5.103 0 + 0.193 5 $\ast$ 1000 = 198.603, representing a sale of $198 603. The estimated regression model concerning equation (1) is given by$$\begin{array}{}\text{(2)}& Y=5.1030+0.1935\text{\hspace{0.17em}Instagram}.\end{array}$$

A visual display (graphical illustration) of the positive linear relationship between Instagram medium and sales is presented in Figure 1. From the visual display in Figure 1, we observe that spending money on Instagram advertising is very fruitful and helps to increase the sale.

[figure omitted; refer to PDF]

To show the usefulness of the NGI-Weibull model, certain statistical tools (STs) are considered. These STs consist of four information criteria (IC) and three goodness-of-fit measures (GFMs) along with the p value. The values of the IC are calculated as follows:

(i) The Akaike IC (AIC)$$\begin{array}{}\text{(39)}& \text{AIC}=2m-2\Delta \mathrm{\Phi },\end{array}$$

(ii) The Bayesian IC (BIC)$$\begin{array}{}\text{(40)}& \text{BIC}=m\log p-2\Delta \mathrm{\Phi },\end{array}$$

(iii) The corrected AIC (CAIC)$$\begin{array}{}\text{(41)}& \text{CAIC}=\frac{2mp}{p-m-1}-2\Delta \mathrm{\Phi },\end{array}$$

(iv) The Hannan–Quinn IC (HQIC)$$\begin{array}{}\text{(42)}& \text{HQIC}=2m\log \log p-2\Delta \mathrm{\Phi },\end{array}$$

  where the terms $p,n$, and $\mathrm{\Delta }\mathrm{\Phi }$ represent the number of parameters, sample size, and LL function, respectively.

The values of the GFMs are calculated as follows:

(i) The Anderson–Darling (AD) test statistic$$\begin{array}{}\text{(43)}& \text{AD}=-p-\frac{1}{p}{\displaystyle \sum _{v=1}^{p}2v-1\log K{z}_v+\log 1-K{z}_{p-v+1}}.\end{array}$$

(ii) The Cramér–von Mises (CM) test$$\begin{array}{}\text{(44)}& \text{CM}=\frac{1}{12p}+{\displaystyle \sum _{v=1}^p{\frac{2v-1}{2p}-K{z}_v}^2}.\end{array}$$

(iii) The Kolmogorov–Smirnov (KS) test$$\begin{array}{}\text{(45)}& \text{KS}={\text{sup}}_z{K}_{p}z-Kz.\end{array}$$

Corresponding to the Instagram sales data, the numerical estimates (NEs) of the model parameters are obtained via implementing the $\mathsf{R-script}$ with the method $\mathsf{SANN}$; see Appendix. The NEs of the fitted models are provided in Table 3, whereas the values of IC measures and GFMs of the fitted models are, respectively, given in Tables 4 and 5.

Table 3

The values of the estimated parameters of the fitted models.

Models	$\lambda$	${\lambda }_1$	${\lambda }_2$	$\beta$
NGI-Weibull	16.910 6	0.9307	20.1934	—
IW	—	2.5589	91.4791	—
Exp-Lomax	—	7.9471	0.0578	10.1876

Table 4

The numerical values of the IC measures of the fitted distributions.

Models	AIC	CAIC	BIC	HQIC
NGI-Weibull	528.2917	528.5181	536.3931	531.5776
IW	553.9948	554.1070	559.3958	556.1855
Exp-Lomax	544.1750	544.4014	552.2765	547.4610

Table 5

The GFMs of the fitted models.

Models	CM	AD	KS	p value
NGI-Weibull	0.0310	0.2742	0.0465	0.9707
IW	0.3138	2.1091	0.1078	0.1544
Exp-Lomax	0.0500	0.4164	0.0977	0.2438

For the underline data, a model with a larger p value and smaller values of IC and GFMs is considered a better model. From the presented results in Tables 4 and 5, it is obvious that the NGI-Weibull model is the best, as it has the smallest values of the IC and GFMs and a larger p value. This fact reveals the applicability and importance of the NGI-Weibull distribution to deal with Instagram sales data and other data sets in the business management and finance sectors.

Besides the numerical illustration, a visual display of the performances of the competing models is presented in Figures 5–8. For the visual comparison, we plotted the graphs of the fitted DFs (Figure 5), SFs (Figure 6), QQ (Figure 7), and PP (Figure 8) of the fitted models. It is important to note that the plots in Figures 5–8 are obtained for NGI-Weibull (red line), IW (blue line), and Exp-Lomax (green line).

[figure omitted; refer to PDF][figure omitted; refer to PDF][figure omitted; refer to PDF][figure omitted; refer to PDF]

4. Concluding Remarks

This work explored the impact of online marketing on sales. Among the available online marketing media, a well-known online medium called Instagram is considered. The data sets related to Instagram advertising and sales were studied and analyzed scientifically. To carry out the analysis, we implemented the linear regression approach along with the F-test and t-test. Based on these tests, it showed that there is a positive impact of Instagram advertising on sales. According to the finding of this study, it showed that spending money on Instagram advertising can increase the sale. In addition to the F-test and t-test, we also performed the CT. Based on the results of the CT, it was observed that there is a positive correlation between Instagram advertising and sales.

Finally, a new statistical model named a NGI-Weibull was introduced and studied in detail. Certain mathematical properties along the HT characteristics of the NGI-Weibull distribution were obtained. The NGI-Weibull was applied to model the Instagram advertising sales data. The comparison of the NGI-Weibull model was made with the other models. Certain statistical tools (AIC, CM, BIC, AD, CAIC, KS, and HQIC) were considered for comparative purposes to see which model provides the best description of the Instagram advertising sales data. Using these statistical tools, it showed that the NGI-Weibull model is the best model for taking care of financial data sets.

Appendix

Appendix

The $\mathsf{R-code}$ is used for analysis under Section 3.

  data=c(11.451, 6.357, 5.186, 7.363, 6.765, 3.683, 7.343, 5.190, 3.009,

  6.398, 5.178, 7.638, 6.240, 5.643, 8.846, 11.673, 5.243, 10.130, 6.725,

  8.010, 7.610, 4.479, 17.753, 9.932, 5.634, 6.151, 7.989, 6.826, 10.195,

  6.006, 11.265, 7.004, 5.477, 8.616, 5.029, 6.600, 13.140, 6.733, 5.594,

  11.294, 7.121, 9.427, 10.728, 7.218, 4.940, 6.648, 4.479, 11.811, 7.945,

  4.079, 6.814, 5.388, 9.145, 11.609, 11.661, 12.514, 3.671, 7.452, 9.028,

  9.157, 4.580, 13.188, 9.028, 7.977, 10.070, 5.796, 5.614, 6.196, 11.011,

  8.038, 9.472, 6.547, 3.546, 4.839, 9.068, 5.566, 2.415, 5.388, 3.473,

  4.625, 6.770, 7.367, 4.645, 5.647, 9.383, 7.892, 7.137, 8.575, 7.630,

  8.922, 6.018, 3.732, 9.912, 11.015, 5.691, 8.620, 6.321, 7.989, 12.614,

  8.967, 6.248, 12.017, 7.767, 7.569, 10.441, 9.730, 3.821, 5.117, 2.968, 10.090)

  ################################################################################

  ##### PDF of the NGI-Weibull distribution

  ################################################################################

  pdf_pm <- function(par,x)

  {

  lam= par[1]

  lam1= par[2]

  lam2= par[3]

  lam1$\ast$lam2$\ast$(x^(-lam1-1))$\ast$exp(-lam2/x^lam1)$\ast$((1-exp(-lam2/x^lam1))^(lam-1))

  $\ast$((1+lam)-exp(-lam2/x^lam1))/exp(exp(-lam2/x^lam1))

  }

  ################################################################################

  ##### DF of the NGI-Weibull distribution

  ################################################################################

  cdf_pm <- function(par,x)

  {

  lam= par[1]

  lam1= par[2]

  lam2= par[3]

  1-(((1-exp(-lam2/x^lam1))^(lam))/(exp(exp(-lam2/x^lam1))))

  }

  set.seed(0)

  goodness.fit(pdf=pdf_pm, cdf=cdf_pm,

  starts = c(0.5,0.5,0.5), data = data,

  method=”SANN,” domain=c(0,Inf),mle=NULL)

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