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Multiple Regression Analysisamazoncom Has Become One Of The Most Succ

Multiple Regression Analysis Amazon.com has become one of the most successful online merchants. Two measures of its success are sales and net income/loss figures. The data can be found in the file, Amazon . Use Excel to complete the following: 1. Construct a scatter plot for Amazon's net income/loss and sales figures for the period 1995–2015. 2. Determine a polynomial model, including its order (or degree), for Amazon's net income/loss and sales figures. Use Word to complete the following: 3. Explain your process of determining the polynomial model 4. Submit your work in a Word document and attach your Excel file.

Paper For Above instruction

In recent years, Amazon.com’s exponential growth has attracted extensive analysis to understand the factors influencing its financial performance over time. This paper addresses the relationship between Amazon’s sales and net income/loss figures from 1995 to 2015 by employing statistical tools such as scatter plots and polynomial regression models. The goal is to visualize the data distribution and identify the most suitable model to describe the relationship between these two variables, thus providing insights into how sales figures influence net income and predicting future trends through polynomial modeling.

Constructing a Scatter Plot

The first step involves visualizing the relationship between Amazon’s sales and net income/loss figures over the specified period. Using Microsoft Excel, the data for sales and net income/loss from 1995 through 2015 are plotted in a scatter diagram. This visualization helps to identify patterns, outliers, and the general trend within the data set.

The scatter plot indicates a non-linear relationship, as the points do not align along a straight line, suggesting the need for a polynomial regression model. Notably, in earlier years, the company experienced minimal or negative net income despite increasing sales, while in later years, a more complex pattern emerges characterized by fluctuations in income as sales continue to grow substantially.

Determining the Polynomial Model

Selecting the appropriate polynomial degree involves iterative testing. Initially, a linear model is fitted to the data to establish a baseline. The residuals—differences between observed and predicted values—are examined to detect patterning or systematic deviation, indicating the inadequacy of a simple linear regression.

Subsequently, quadratic (second-degree) and cubic (third-degree) models are fitted, with each model’s goodness-of-fit assessed using statistical metrics such as R-squared, adjusted R-squared, and analysis of residual plots. For this dataset, a quadratic model demonstrates a better fit than the linear model, capturing the curve observed in the scatter plot. The residuals from the quadratic model display random dispersion, suggesting a suitable fit. A cubic model does not significantly improve the fit and tends to overfit the data, leading to potential model complexity without precise benefits.

Based on this process, the quadratic polynomial model is identified as the most appropriate for predicting Amazon’s net income/loss based on sales figures over the period. This model captures the nonlinear growth and fluctuations inherent in the data and provides a foundation for interpretation and forecasting.

Explaining the Model Selection Process

The process of determining the best polynomial model involved visual inspection, residual analysis, and statistical validation. Initially, visual assessment of the scatter plot indicated a non-linear trend, prompting considerations of quadratic and higher-order models. Comparing models involved examining R-squared values, with the quadratic polynomial achieving a higher value than the linear model, indicating a better fit.

Residual plots for each model were analyzed for randomness; the quadratic model’s residuals appeared randomly dispersed around zero, confirming its appropriateness. Further, statistical tests to avoid overfitting favored the quadratic model as the optimal compromise between model complexity and fit quality.

This systematic approach ensures the selected model reliably describes the relationship between Amazon's sales and net income/loss figures and can serve as a tool for future predictions and strategic planning.

Conclusion

Analyzing Amazon’s financial data from 1995 to 2015 through scatter plotting and polynomial modeling reveals a complex, nonlinear relationship between sales and net income/loss. The quadratic model offers a robust fit, facilitating better understanding of the company's growth dynamics. Employing such models helps stakeholders anticipate future performance trends based on sales data, enabling more informed strategic decisions, especially in an ever-evolving e-commerce landscape.

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