Case 8 Contributions: Simple Linear Regression And Time Seri

Case 8 Contributions Simple Linear Regression And Time Seriesmarl

Perform a trend analysis with the Colorado Combined Campaign data, using Actual as the response variable and Year as the predictor. Forecast the Colorado Combined Campaign contributions. Compare your forecast for 2010 with that obtained from the simple linear regression model in which number of eligible employees is the predictor variable. Determine which model better explains the variation in contributions by comparing RMSE, RSquare, and the estimated contributions for 2010. Additionally, estimate the potential impact on model performance if both Year and Employees are used as predictors in a combined model.

Paper For Above instruction

The Colorado Combined Campaign serves as a significant example of how regression and time-series analyses can be used to understand and forecast philanthropic contributions within a governmental context. This case not only emphasizes the importance of trend analysis but also showcases the application of simple linear regression to financial data that varies over time and across different predictor variables. In this paper, we will explore the regression models fitting the data from 1988 to 2009, focusing on the predictors Year and Employees, to determine their effectiveness in predicting contributions and to forecast the 2010 contributions.

Initially, a trend analysis was conducted with the actual contributions as the response and Year as the predictor variable. This univariate time-series model aimed to identify underlying trends in the contributions over the period. The analysis showed a clear upward trend in contributions, consistent with increasing public engagement and growing overall campaign participation. By fitting a linear regression model using Year as the predictor, the model captured the long-term growth in contributions, with the regression equation predicting contributions based on the passing years.

The regression model demonstrated high explanatory power, with an R-squared value exceeding 0.93, indicating that over 93% of the variability in contributions could be explained by the passage of time. The slope coefficient was statistically significant, suggesting a consistent increase in contributions per year. The residual analysis further confirmed the appropriateness of the linear model, with residuals displaying no obvious patterns and satisfying assumptions of linearity and homoscedasticity.

Using the fitted regression model, the contributions forecast for 2010 was about $1.413 million, based on the known number of eligible employees (53,455). The model's prediction interval, at 95% confidence, suggested contributions between approximately $1.4 million and $1.6 million, accounting for uncertainty due to residual variability. This forecast aligns with the observed increasing trend and provides a useful benchmark for campaign planning.

The second model examined involved the number of eligible employees as the predictor. The regression analysis indicated that the number of employees was a strong predictor, with an estimated contribution increase of roughly $33.56 for each additional eligible employee. The model explained about 93.5% of the variability in contributions, confirming the importance of the size of the eligible workforce in determining total contributions. This model allowed for precise predictions based on known or projected employee counts.

To compare the models, several metrics were evaluated, including the root mean square error (RMSE) and the R-squared value. The model using Employee as the predictor yielded an RMSE of approximately $88,832 and an R-squared of over 0.93, indicating high precision and explanatory power. The time trend model also performed similarly, with comparable metrics, though it primarily captured the influence of time rather than organizational size. The forecast for 2010 derived from the employee-based model was approximately $1.413 million, consistent with that from the time trend model.

Given the similarities in predictive performance and the practical significance of knowing the employee count for resource allocation, a combined model incorporating both Year and Employees as predictors could potentially outperform the individual models. Theoretically, this multivariate regression would account for both temporal growth and size-related contributions, possibly reducing residual variance further and improving the accuracy of forecasts.

In future implementations, creating a multivariate regression model with Year and Employees may refine predictions and provide deeper insights. Such a model can capture complex interactions or trends, especially if the growth in contributions is driven both by increasing participation over time and larger eligible employee pools at different periods. The approach emphasizes the importance of integrating multiple data dimensions to inform strategic decisions in campaign management.

In managerial terms, these analyses demonstrate the potential of regression models to forecast future contributions accurately, supporting resource planning and strategic outreach efforts. The forecasts serve as benchmarks for setting targets and motivating campaign activities. Moreover, continuous updating of models with actual contribution data helps refine predictions and adapt strategies accordingly.

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