Take Test Week 7 Linear Regression Mat510076va016

11112018 Take Test Week 7 Linear Regression Mat510076va016 Htt

This assignment involves analyzing data from a study conducted by an insurance company to examine the effect of changing the claims approval process on policyholder satisfaction, as measured by the average time required to approve and mail claims. The data compares the old and new processes over 12 weeks each, with the goal of assessing improvements attributable to the new process through linear regression analysis. Tasks include deriving regression equations for both processes, interpreting model coefficients, evaluating correlation and variability, and quantifying the impact of the process change.

Paper For Above instruction

The insurance company’s study aimed to determine whether modifying the claims approval process could reduce the average time for claim settlement, thereby improving policyholder satisfaction. To analyze the impact, the company collected weekly data on the average approval times before and after the implementation of the new process. The primary statistical method employed was linear regression, which facilitates understanding the relationship between the process type and approval times, quantifying the effect of process changes, and evaluating the consistency and reliability of the observed improvements.

First, linear regression equations were generated for both the old and the new processes. These equations model the expected approval times based on the process type, with the regressions providing intercepts and slopes that characterize the baseline and incremental effects. For the old process, the regression equation was identified as y = 29.3 + 0.514x, where the intercept (29.3) indicates the predicted approval time when the explanatory variable is zero, and the slope (0.514) reflects how approval time varies with changes in the process variable. For the new process, the regression equation was y = 30.3 - 0.57x, with the intercept representing the baseline approval time and the negative slope indicating a potential decrease in approval time with adjustments in the process variable.

Interpreting the slopes of these equations provides insights into how process modifications influence approval times. The slope of 0.514 in the old process suggests that for each unit increase in the process variable, there is an approximate increase of 0.514 days in the average approval time, implying a positive association. Conversely, the slope of -0.57 in the new process indicates that an increase in the process variable correlates with a decrease of approximately 0.57 days in approval time, demonstrating an improvement in efficiency.

The intercepts serve as the estimated average approval times when the process variable is zero. In the old process, an intercept of 29.3 indicates the predicted approval time absent any influence from the process variable, while in the new process, the intercept of 30.3 suggests a slightly higher baseline approval time. These values provide reference points for understanding the magnitude of change brought about by the process modifications.

Correlation coefficients quantify the strength of the linear relationships. For the old process, the correlation coefficient was approximately 0.481, indicating a moderate positive relationship between the process variable and approval time. For the new process, the correlation coefficient was around 0.603, reflecting a slightly stronger association and suggesting that the process variable explains a greater portion of the variability in approval times post-implementation.

The coefficient of determination (R-squared) was calculated to assess the proportion of variability in approval times explained by the process variables. For the old process, R-squared was approximately 0.231, meaning about 23.1% of the variability could be explained by the model. For the new process, R-squared was approximately 0.363, indicating a better fit and that 36.3% of the variance in approval times was attributable to the process variable, supporting the conclusion that changes in the process had a significant impact.

Further analysis involved examining the coefficient of variation, which measures relative variability. For the old process, a coefficient of variation of about 23.1% was observed, while the new process exhibited a higher coefficient of 36.3%. This increase suggests greater relative variability in approval times under the new process, potentially due to implementation inconsistencies or other factors affecting process stability.

Evaluating the overall effect of the process change, the data reveals a decrease in the average approval time from approximately 33.5 days to 26.35 days, amounting to a reduction of about 7.15 days. This substantial decrease underscores the positive impact of the process modification on policyholder satisfaction. The analysis indicates that the new process not only reduced the mean approval time but also improved the efficiency, as confirmed by the regression results and higher R-squared values.

In conclusion, the application of linear regression analysis provided valuable insights into the effects of the process change. The regression equations quantified the relationship between process modifications and approval times, with negative slopes post-change indicating improved efficiency. The increased correlation and coefficient of determination further validated the significance of these improvements, supporting the decision to adopt the new process for enhanced policyholder satisfaction and operational efficiency.

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