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Econometrics Report
The largest problem in todays businesses and firms is to predict the future demand and sales with the highest level of accuracy. This problem is common in the industries which face great competition. One of such industries is technological industry, which according to McElveen (2013), it is the largest and fastest growing industries in the United States of America. The same report reveals that since the year 2000, the demand for mobile phones has been on the rise, and this has facilitated the upcoming of several firms which deal with production and distribution of phones. The technological industry has over 100 firms which produce products with varying properties and prices. Therefore, it is clear that each company should try and come up with a unique methodology of determining the future market demand, so that it can always remain at the top of the scale, above its competitors. There are several factors which affect the demand for any commodity. Some of these factors include the price of that commodity, the competitors price, the inflation of that country, the poverty and the GDP of state. Therefore, this paper will use multiple regression analysis in trying to predict the future demand for mobile phones, with the analysis of a case study of Apple.
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Background Information of Apple Company
Apple is a multinational corporation which was founded by Steve Jobs and Steve Wozniak in California in the year 1975. The two founders had an aim of making computers which are small enough to be used by people in their homes. This company deals with both computer hardware and software. It produces consumer electronics, computer servers, and personal computers among others. Apples main product is the iPhone smartphone, which has several varieties. After the introduction of iPhone in the market, the income of Apple Inc. grew from $150 Billion in 2013 to $510 Billion in 2014 (Kumar, Kim, & Helmy, 2013). The most current models of iPhone are the iPhone 6s and iPhone 6s Plus. Apart from these products, the company also produces iPads, iPods, smart watches, and MacBooks, among others.
This paper primarily discusses the sales of the Apple mobile phones, since this is the primary commodity produced by this company. West and Mace (2007) explain why Apple products are more expensive than similar products from other companies. Apple products also have more advanced features, and they are more durable. Also, the same study reveals that more than 25% of the young people, aged between 18 and 34 years old in the United States of America own at least one product from Apple Inc.
Also, a study by Kumar et al. (2013) shows that Apple products are not common in second and third world countries, where only less than 2% of the population own Apple devices. This fact shows that it is important for Apple to consider conducting an indepth research which will enable the company to penetrate into these markets. Therefore, this is the main reason for conducting this research, because the main aim of the study is to come up with a model which can predict the demand for mobile phones. The model is applicable in all states, including lowincome countries, and it is possible to vary the variables of interest, so as to observe the result. The model will also be able to predict the future values, given the present and previous data.
Variables
The main aim of this study is to use regression analysis to predict the sales of mobile phones in Apple Inc. On the one hand, the dependent variable is the demand for mobile phones. On the other hand, the independent variables are the average prices of a cell phone in Apple. Other important variables besides the price of a mobile phone in the Apples competitors are the poverty rate, and inflation and GDP of the United States of America.
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Research Objectives
 To find the correlation between the demand for mobile phones and price of Apple products, the price of competitors products, the poverty rate, inflation rate and GDP.
 To determine which variables among the price of the mobile phone of Apple, prices of competitors, the inflation rate, poverty rate and GDP have a significant influence on the demand for smart phones.
 To come up with a model which will predict the demand for Apples products, given the explanatory variables of interest.
Research Question
 Is there a significant correlation between the demand for mobile phones and price of Apple products, the price of competitor products, the poverty rate, inflation rate and GDP?
 Is there a linear relationship between the demand for mobile phones and prices of Apple products, the prices of competitor products, the poverty rate, inflation rate and GDP?
Research Hypothesis
 Ho (Null hypothesis): There is no significant correlation between the demand for mobile phones and prices of Apple products, the price of competitor products, the poverty rate, inflation rate and GDP.
 Ha (Alternative hypothesis): There is a significant correlation between the demand for mobile phones and price of Apple products, the price of competitors products, the poverty rate, inflation rate and GDP.
 Ho (Null hypothesis): There is no significant linear relationship between the demand for mobile phones and price of Apple products, the price of competitor products, the poverty rate, inflation rate and GDP.
 Ha (Alternative hypothesis): There is a significant linear relationship between the demand for mobile phones and price of Apple products, the price of competitor products, the poverty rate, inflation rate and GDP.
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Data Collection
This paper uses quantitative research methodology, which according to Anderberg (2014), it is a research design which yields numerical data. Therefore, the researcher collects data of the data type interval or ratio from both the government database and the sample of respondents. This research uses the data from the year 2000 to 2014. On the one hand, data on the poverty rate, inflation rate, and the GDP is collected from the government database. On the other hand, the researcher uses a survey tool to collect the data on demand, and the prices of mobile phones of Apple and competitors. The target population comprises of the sellers, and distributors of the mobile phones in five states of United States of America, and individuals who have been in operation since the year 2000, so as to make sure that all people in the sample have the 15 year period data. The states of interest to this research include California, Hawaii, Texas, Alaska, and Florida. Therefore, this paper applies cluster sampling, which is the sampling technique where the target population is naturally divided into several homogeneous groupings, and then the researcher collects simple random samples from each of the groupings (Shorack & Wellner, 2009). The researcher collects samples of ten individuals from each of the groupings (states) and gives each of the respondents the survey with questions.
Data Analysis
After the respondents record their responses in the survey tool, the researcher recorded the responses in Excel with the purpose of data cleaning and preliminary data analysis. The preliminary analysis process involved averaging the data for each of the respondents, so as to obtain one dataset. Table 1 below gives the final clean data for all the variables in 15 years.
Table 1: Clean Data
Year 
Quantity Demanded (In Thousands)  Average Price of a Mobile Phone in Apple  Average Competitors Price  Poverty Rate  Inflation 
GDP ($100B) 
2000  25.5  128.75  105.9612500  0.1968504  2.1880272  76.6406000 
2001  28.56  139.05  114.4381500  0.1953125  3.3768573  81.0020100 
2002  30.6  154.5  127.1535000  0.1937984  2.8261711  86.0851500 
2003  32.64  185.4  152.5842000  0.1923077  1.5860316  90.8916800 
2004  35.7  216.3  178.0149000  0.1908397  2.2700950  96.6062400 
2005  36.72  329.6  271.2608000  0.1906941  2.6772367  102.8477900 
2006  38.76  334.75  275.4992500  0.1905488  3.3927468  106.2182400 
2007  40.8  334.75  275.4992500  0.1904037  3.2259441  109.7751400 
2008  45.9  360.5  296.6915000  0.1902588  2.8526725  115.1067000 
2009  59.16  365.65  300.9299500  0.1901141  3.8391003  122.7492800 
2010  79.56  368.74  303.4730200  0.1899696  0.355546  130.9372600 
2011  91.8  376.98  310.2545400  0.1898254  1.6400434  138.5588800 
2012  104.04  391.4  322.1222000  0.1896813  3.1568416  144.7763500 
2013  153  412  339.0760000  0.1895375  2.0693373  147.1858200 
2014  183.6  415.09  341.6190700  0.1893939  1.4648327  144.1873900 
Correlation Analysis
The paper uses correlation analysis technique to answer the first hypothesis. The researcher uses SPSS version 21 in finding the correlation between all of the variables under study. Table 2 below shows the correlation matrix
Table 2: Correlation Matrix
Quantity Demanded (In Thousands)  Average Price of a Mobile Phone in Apple  Average Competitors Price  Poverty Rate  Inflation  GDP ($100B)  
Quantity Demanded (In Thousands)  Pearson Correlation  1  .705**  .555**  .579*  .355  .858** 
Sig. (2tailed)  .003  .004  .024  .194  .000  
N  15  15  15  15  15  15  
Average Price of a Mobile Phone in Apple  Pearson Correlation  .705**  1  1.000**  .913**  .136  .928** 
Sig. (2tailed)  .003  .000  .000  .630  .000  
N  15  15  15  15  15  15  
Average Competitors Price  Pearson Correlation  .555**  1.000**  1  .913**  .136  .928** 
Sig. (2tailed)  .004  .000  .000  .630  .000  
N  15  15  15  15  15  15  
Poverty Rate  Pearson Correlation  .579*  .913**  .913**  1  .153  .839** 
Sig. (2tailed)  .024  .000  .000  .585  .000  
N  15  15  15  15  15  15  
Inflation  Pearson Correlation  .355  .136  .136  .153  1  .272 
Sig. (2tailed)  .194  .630  .630  .585  .327  
N  15  15  15  15  15  15  
GDP ($100B)  Pearson Correlation  .858**  .928**  .928**  .839**  .272  1 
Sig. (2tailed)  .000  .000  .000  .000  .327  
N  15  15  15  15  15  15  
**. Correlation is significant at the 0.01 level (2tailed).  
*. Correlation is significant at the 0.05 level (2tailed). 
The above analysis reveals that there is a significant negative correlation between quantity demanded and the average price of Apple phone (Pearson Correlation=0.705, p=0.003), implying that an increase in the price of Apple products leads to a decrease in demand. On the one hand, there is a significant positive correlation between the prices of competitors products and the demand for Apple products (Pearson Correlation=0.555, p=0.004) showing that an increase in the price of competitors products leads to an increase in the demand for Apple phones. On the other hand, the poverty rate negatively correlates with the demand, and the correlation is significant at 5% level (Pearson Correlation=0.579, p=0.024). This result implies that an increase in the rate of poverty of people leads to a decrease in the demand for mobile phones. Lastly, there is no significant correlation between the demand and the inflation rate, but the correlation between the GPD and the demand is positive and significant at 5% level (Pearson Correlation=0.858, p<0.000). Therefore, an increase in the GDP leads to an increase in the sales/demand for Apple products. Since a significant correlation exists between most of the variables, it is, therefore, appropriate to conduct the regression analysis.
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Multivariate Regression Analysis
This paper uses a regression model with the dependent variable as the demand, and explanatory variables are the price of Apples products, the demand for competitors products, the poverty rate, inflation and GDP of the United States of America. Tables 3, 4 and 5 give the output of the model.
Table 3: Model Summary Statistics
Model 
R  R Square  Adjusted R Square  Std. Error of the Estimate 
DurbinWatson 
1  .904a  .817  .743  24.48733  .611 
a. Predictors: (Constant), GDP ($100B), Inflation, Poverty rate, Average Competitors Price  
b. Dependent Variable: Quantity Demanded (In Thousands) 
Table 4: ANOVA Table
Model 
Sum of Squares  df  Mean Square  F 
Sig. 

1  Regression  26709.446  4  6677.361  11.136  .001b 
Residual  5996.291  10  599.629  
Total  32705.737  14  
a. Dependent Variable: Quantity Demanded (In Thousands)  
b. Predictors: (Constant), GDP ($100B), Inflation, Poverty rate, Average Competitors Price 
Table 3 reveals that there is 74.3% of the variation in the demand for Apple products, which is explained by the explanatory variables (Adjusted R Square=0.743). Table 4 shows that a linear model is significant in modeling this data (F(4,10)=11.136, p=0.001). This result implies that there is at least one of the explanatory variables, which has a significant linear relationship with the dependent variable. From the output in the Table 5, it is clear that the average price of mobile phones in Apple has a significant negative linear relationship with the demand (b=1.68, t=1.36, p=0.008). This result implies that an increase in the price of a phone by $1 leads to a decrease in demand by 1.68 thousand units. Also, there is a significant positive relationship between demand and prices of competitors (b=2.213, t=1.48, p=0.002), implying that an increase in the competitors price by $1 leads to an increase in the Apples demand by 2.213 thousand units. Table 5 also shows that the poverty rate has a significant negative relationship between the dependent variable (b=67.36, t=1.015, p=0.007), implying that an increase in the poverty rate by 1% leads to a decrease in the dependent variable by 67 thousand units. Lastly, the poverty rate does not have a significant relationship with the demand, while the GDP has a significant positive correlation with the demand (b=2.715, t=3.6, p=0.05). This result shows that an increase in GDP by $100 billion leads to an increase in the demand by 2.715 thousand units.
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Where
X1= Average price of a mobile phone in Apple
X2= Average competitors price
X3= Poverty rate
X4=Inflation rate
X5= GDP ($100B)
Model Diagnostics
Figures 1 and 2 below show the probability plots and residual plots, respectively. The probability plot tests the assumption of linearity of the variables, while the residual plot tests the assumption of homoscedasticity of residuals (Anderberg, 2014). Figure 1 reveals that the linearity assumption is satisfied, since the plots scatter around the straight line. Also, the data satisfies the homoscedasticity assumption, since the residuals scatter around the zero line. Therefore, the data satisfies all of the assumptions, and the linear model is applicable for this dataset.
Figure 1: Probability plot
Figure 2: Residual plot
Residual Output
Table 6 shows the residual output of the data. From the output, it is clear that the residuals are not very far from zero. Also, the residuals alternate between positive values and negative values. Therefore, the residuals show that the data is accurate, and the results can be trusted.
Table 6: Residual Output
Predicted Demand  Residual 
28.99101  3.49101 
20.15694  8.40306 
29.96522  0.63478 
33.25628  0.61628 
29.42235  6.27765 
48.73847  12.0185 
28.77784  9.98216 
38.67252  2.12748 
51.32272  5.42272 
63.10093  3.94093 
92.67194  13.1119 
118.6674  26.8674 
121.385  17.345 
154.2204  1.22043 
126.991  56.60904 
Economic Implications, Recommendations, and Conclusion
This model has several economic implications. First, the dependent variable in the above model is the demand for mobile phones. The increase in demand has several positive implications on the GDP and the per capita income. Also, this research can be replicable in other companies which are not necessarily affiliated with Apple because the results have revealed that the coefficients are significant. Through this, the productivity of the technological industry can improve, thus increasing the economy of the country.
This paper recommends that other research works should be done on this topic, while taking into consideration several other confounding variables. A confounding variable is a factor which indirectly affects the dependent variable, but they are not of interest to the researcher. These variables include the features and properties of the mobile phone, the capital base of the company and the advertisement expenditures of the form. The inclusion of these variables in the model improves the accuracy of the model and the accuracy of the predicted values. Also, research works should focus on conducting an investigation in the lowincome countries, so as to have a solid model which fits those areas.
In conclusion, it is clear from the results above that there is a negative correlation between the demand and the price of Apple products, the poverty level, and the inflation rate. Also, the results reveal that there exists a positive correlation between the competitors prices and the GDP of that country. Lastly, the regression analysis shows that there is a significant positive relationship between the demand for Apples commodities and the competitors prices and GDP. Also, there is a negative linear relationship between the demand and the prices of Apple products and poverty late, but the inflation rate does not show any possibility of a significant relationship. Therefore, Apple should use this model in predicting its sales to ensure its plans for the future.
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