Correlation between Instagram followers and celebrity earnings

Relationship between Instagram Following and Salary

Research question Is there a relationship between top celebrities' and fashion models' Salary and their Instagram following?

Introduction

Social media growth has impacted many people's lives, especially celebrities and fashion designers. Instagram is one of these platforms where celebrities maximize their influence by showcasing various fashion and designs from various parts of the globe. In December 2021, when I watched the model of the year awards, I noticed that most celebrities who earn a lot of money have a huge following on their social accounts, such as Instagram. Through this information, I decided to compute the correlation between celebrities' Instagram following and SalarySalary.

Mathematical exploration In this IA, various mathematical tools will be applied. Some of these tools include the

Pearson correlation method, which will be used to find the direction and strength of the relationship. The scatter plot is used to represent raw data in graphical form, which also shows the direction of the correlation (positive or negative). An uphill trend shows a positive correlation, while a downhill trend shows a negative trend. After data collection, I will also use the collected data to find the mean and standard deviation.

Hypothesis

In this exploration, I predict that there is a positive association between Instagram following and celebrities' salaries. As Instagram following increases, the salary also increases. The scatter graph will have a positive graph line, still confirming the positive correlation between Instagram following and Salary.

Aim

This internal assessment aims to use mathematical tools to find the relationship between celebrities' salary and their corresponding Instagram following. Some of the mathematical tricks used include; Pearson correlation, scatter graph, and Chi-square methods.

Raw data

To compute the relationship between fashion models' salaries and Instagram following, I collected data for the top 15 celebrities in the world. The data will comprise 5 models from England (Europe), the United States of America (Central America), and Brazil (South America), as recorded in table 1 below;

Name

Nationality

Instagram followers (million)

Salary (million USD) Gisele Bündchen

Brazil 18.5 40.0

Adriana Lima

Brazil 13.9 11.0

Alessandra Ambrosio

Brazil 10.7 10.4

Isabeli Fontana

Brazil 1.2 4.0

Ana Beatriz Barros

Brazil 0.451 1.0

Kendall Jenner

American 21.7 40.0

Bella Hadid

American 48.9 19.0

Statistical Analysis Based on the data above, I decided to use a mathematical approach to calculate the mean/ average and the standard deviation.

Mean This is the average value of the total dataset, and it can be calculated using the following;

Given = average/mean = Instagram followers and SalarySalary =Total number of models I used the above formula to develop the following table; Table 2: Average/mean table

Adriana Lima

American 13.9 11.0

Chrissy Teigen

American 36.8 12.0

Liu Wen

American 5.5 7.0

Cara Delevingne

England 43.4 10.73

Rosie Huntington

England 14.5 8.71

Kate Moss

England 1.3 6.72

David Gandy

England 1.0 5.37

Naomi Campbell

England 12.1 4.0 A=∑x n A x N It can be noted that, on average, each celebrity has 29.27million followers, and at the same time, each celebrity earns an average of 12.667 USD.

Standard deviation

Instagram following (million)

Salary (million USD) 18.5 40.0 13.9 11.0 10.7 10.4 1.2 4.0 0.451 1.0 40.0 48.9 19.0 13.9 11.0 36.8 12.0 5.5 7.0 43.4 10.73 14.5 8.71 1.3 6.72 1.0 5.37 12.1 4.0 439.151 ∑x= 190.93 ∑x= A.m(instagram)followers =439.151 15 = 29.27million A.m(salar y)=190.93 15 =$12.667million The formula to calculate the standard deviation is given below; (McGrath et al., 2020) Where; = S.D N= number of celebrities = individual value (Instagram followers and SalarySalary) Applying the above formula, I developed the following table;

Instagram (million)

Salary (million USD) 18.5 115.9929 744.1984 13.9 236.2369 2.9584 10.7 344.8449 10.4 5.3824 1.2 787.9249 76.0384 0.451 830.534761 137.3584 35242.5529 744.1984 48.9 385.3369 39.4384 13.9 236.2369 2.9584 36.8 56.7009 0.5184 5.5 565.0129 32.7184 43.4 199.6569 10.73 3.9601 14.5 218.1529 8.71 16.0801 ∑(x1−μ)2 ∑(x1−μ)2

Chi-square This is a method that is used to find the level at which variables depend on each other. The formula to calculate Chi-square; (Connelly, 2019) Given that; =hypothetical value Prior to computing the correlation coefficient, it is imperative to state both the alternative and null hypotheses, as shown below; H0 =Salary is independent of the Instagram following (µ≤0.5) H1= SalarySalary is dependent on the Instagram following (µ>0.5) 1.3 782.3209 6.72 799.1929 5.37 54.0225 12.1 294.8089 76.0384 41095.5074 1971.869 σ(instagramfollowing) = 41095.5074 15 = 52.34 (Salar y) = 1971.869 15 = 11.46 x2=∑(0i 2−Ei 2)

Ei Ei=Listedvalue 0i x2=Chi −squaredvalue I applied the topic above to develop the following table; The chi-square from the above table is 154.9436, which is> 0.5. Thus the alternative hypothesis, which states that "Salary is dependent on the Instagram following," will be adopted. The null hypothesis states that "Salary is independent of the Instagram following" will be ignored.

Pearson correlation (million)

Observed value (O)

Expected value (e) 18.5 12.728 112.9791 13.9 12.728 -3.2214 10.7 10.4 12.728 -4.2302 1.2 12.728 -11.4709 0.451 12.728 -12.6494 21.7 12.728 112.9791 48.9 12.728 15.63466 13.9 12.728 -3.2214 36.8 12.728 -1.41436 5.5 12.728 -8.87822 43.4 10.73 12.728 -3.68236 14.5 8.71 12.728 -6.76759 1.3 6.72 12.728 -9.18004 5.37 12.728 -10.4624 12.1 12.728 -11.4709 154.9436

Chi-square x2=(0i 2−Ei 2)

Ei

The Pearson method is used to calculate the relation between dependent and independent variables within a dataset. To compute the correlation coefficient of the above data; Where; = link between salary and Instagram following = Instagram following

Average number of Instagram followers

Model's Salary = average model's SalarySalary I used the above formula to develop the following table; r=∑(x− x)(y− ȳ) [∑(x−x2)(y− ȳ2)] r X x= y= ȳ followers (x)

Salary dx(x-x !) dy (y- ȳ) dxdy (dx)2 (dy)2 18.5 -10.77 27.28 -293.806 115.9929 744.1984 13.9 -15.37 -1.72 26.4364 236.2369 2.9584 10.7 10.4 -18.57 -2.32 43.0824 344.8449 5.3824 1.2 -28.07 -8.72 244.7704 787.9249 76.0384 0.451 -28.819 -11.72 337.7587 830.5348 137.3584 187.73 27.28 5121.274 35242.55 744.1984 48.9 19.63 6.28 123.2764 385.3369 39.4384 13.9 -15.37 -1.72 26.4364 236.2369 2.9584 r =0.701

From the computation above, it is worth noting that the association coefficient is 0.701. This clarifies that there is a strong positive correlation between the variables; whereas Instagram follows advances, the Salary also increases.

Scatter plot The data in table 1 can be plotted in a scatter plot, as shown in figure 1 below; 36.8 7.53 -0.72 -5.4216 56.7009 0.5184 5.5 -23.77 -5.72 135.9644 565.0129 32.7184 43.4 10.73 14.13 -1.99 -28.1187 199.6569 3.9601 14.5 8.71 -14.77 -4.01 59.2277 218.1529 16.0801 1.3 6.72 -27.97 -6 167.82 782.3209 5.37 -28.27 -7.35 207.7845 799.1929 54.0225 12.1 -17.17 -8.72 149.7224 294.8089 76.0384 29.27673 12.72867 6316.208 41095.51 1971.869

Salary&&(million&USD)&vs&instagrm&following

Salary (million USD) 12,5 37,5

Instagram following y&=&0,1537x&+&8,229 R²&=&0,4923

From the graph in the figure above, it can be realized that as the number of Instagram following escalates, the SalarySalary also increases. The graph line above indicates an escalation trend, still confirming that there is a positive link between Instagram following and Salary. The coefficient value from the scatter plot above is; The coefficient value from the above computation is 0.701, indicating that there is a positive correlation between Instagram following and Salary. The calculation concludes that there is a positive link between the two variables and thus confirms my hypothesis, which stated that "there is a positive correlation between celebrity earnings/salary and Instagram following."

Conclusion

The primary objective of this internal assessment was to investigate if there is a relationship between celebrity salary and Instagram following. Before the exploration, I predicted that "there is a positive correlation between celebrity earnings/salary and Instagram following." Various methodologies were used to calculate the coefficient, such as; scatter graphs and Pearson methods. In both methods, it was evident that there is a strong positive association/correlation between celebrities' salaries and Instagram following. As the Instagram following increases, the celebrity's SalarySalary also increases and thus confirming my hypothesis.

Evaluation R2= 0.4923 R= 0.4923 R= 0.701 The IA was great as the aim, "to use mathematical tools to find the relationship between celebrities' salary and their corresponding Instagram following," was achieved. However, various reasons have contributed to some errors in this exploration. There are various social media platforms such as; Facebook, YouTube, and Tiktok platforms. In this exploration, only the Instagram platform was used. In future exploration, the research should also consider the relationship between salary and social media following.