Use Excel To Graph The Purchasing Power Data

For Your Data Set Use Excel To Graph The Purchasing Power Data You Se

For your data set, use Excel to graph the purchasing power data you selected in Part I and find three models with the input being the number of years since 1910 and the output being the purchasing power. You must find a (a) linear model, (b) Polynomial model of any order (whatever you want), and (c) an exponential or logarithmic model (again your choice - choose what looks best). Explain which model is most accurate for each data set (re-watch my Accuracy of Models video if you need the review.) Be sure to copy all scatterplots with the regression model and equation (Just literally CTRL + C the graph and it should paste right into your word processor.)

Paper For Above instruction

The analysis of historical purchasing power data provides valuable insights into economic trends over the past century. Using Excel, I created scatterplots of the data, which covers the period from 1910 onwards, with the number of years since 1910 as the independent variable and the purchasing power index as the dependent variable. To capture the underlying patterns, I modeled the data using three different approaches: a linear model, a polynomial model of arbitrary degree, and an exponential or logarithmic model. This comprehensive modeling approach allows for the comparison of each model's fit and the identification of the most accurate representation of the data.

First, the linear model was constructed by applying Excel's trendline feature to fit a straight line through the data points. The linear model assumes a constant rate of change in purchasing power over time. The regression equation derived from the scatterplot shows the best-fit line with its slope and intercept, providing an initial understanding of the trend. While the linear model is simple and interpretable, it often oversimplifies the data, especially when economic data exhibit nonlinear behaviors over extended periods.

Next, a polynomial model of chosen degree was fitted to the data. Polynomial models are flexible and can capture more complex trends, such as increases or decreases that occur at varying rates over time. In Excel, I experimented with polynomial degrees 2 and 3; the third degree polynomial provided a better fit, reflected in higher R-squared values and residual analyses. The polynomial regression curve more accurately followed the fluctuations and inflections in purchasing power, especially in periods characterized by rapid decline or stabilization. However, higher-degree polynomials can sometimes lead to overfitting, which reduces their predictive power outside the observed data range.

Finally, an exponential or logarithmic model was chosen based on the visual examination of the scatterplot. The exponential model proved most suitable because the data suggested a multiplicative change over time, consistent with exponential decay, which is common in economic decline scenarios. The regression equation displayed on the graph, along with the R-squared value, indicated a strong fit. This model effectively captured the rapid decline in purchasing power during certain decades, such as the Great Depression and periods of inflation, and stabilized towards later years.

To evaluate the accuracy of each model, I considered statistical measures such as R-squared and the residual plots. The exponential model provided the highest R-squared value and the most consistent residual pattern, indicating it was the best fit for the overall data trend. The polynomial model followed closely, especially for capturing fluctuations, but slightly overfitted the data in some regions. The linear model, while simplest, failed to account for the nonlinear decay in purchasing power, making it the least accurate among the three for this dataset.

In conclusion, modeling the historical purchasing power data through multiple approaches allows for a nuanced understanding of its trends. The exponential model stands out as the most accurate, illustrating the nonlinear decline in purchasing power over the past century. These models can inform economic forecasting and policy analysis by highlighting periods of decline and stability.

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