Questions: A financial analyst constructs a statistical model to represent the market shares of several similar companies. She then collects data over the next month to evaluate her model. At the end of the month, she finds that for one of the companies, the difference between her model and the data is 5%. She decides to collect data for an additional two months. If her model is valid, what could she expect from the total data collected after three months? A. The difference between the data and the model will stay the same. B. The difference between the data and the model will get larger. C. The difference between the data and the model will get smaller. D. It is impossible to predict how the difference between the data and the model will change.

A financial analyst constructs a statistical model to represent the market shares of several similar companies. She then collects data over the next month to evaluate her model. At the end of the month, she finds that for one of the companies, the difference between her model and the data is 5%.

She decides to collect data for an additional two months. If her model is valid, what could she expect from the total data collected after three months?
A. The difference between the data and the model will stay the same.
B. The difference between the data and the model will get larger.
C. The difference between the data and the model will get smaller.
D. It is impossible to predict how the difference between the data and the model will change.

Transcript text: A financial analyst constructs a statistical model to represent the market shares of several similar companies. She then collects data over the next month to evaluate her model. At the end of the month, she finds that for one of the companies, the difference between her model and the data is $5 \%$. She decides to collect data for an additional two months. If her model is valid, what could she expect from the total data collected after three months? A. The difference between the data and the model will stay the same. B. The difference between the data and the model will get larger. C. The difference between the data and the model will get smaller. D. It is impossible to predict how the difference between the data and the model will change.

Solution

Solution Steps

To determine the expected outcome, consider the nature of statistical models and data collection. The difference between the model and the data can change due to various factors such as market dynamics, model accuracy, and data variability. Without additional information, it is not possible to predict how the difference will change over time.

Step 1: Understanding the Problem

The financial analyst has a statistical model that shows a $5\%$ difference from the actual data for one of the companies after one month. She plans to collect data for an additional two months and wants to know how this difference might change.

Step 2: Analyzing the Options

The options provided are:

A. The difference will stay the same.
B. The difference will get larger.
C. The difference will get smaller.
D. It is impossible to predict how the difference will change.

Given that statistical models can vary in accuracy and that market conditions can change, it is not possible to definitively predict the behavior of the difference over time without further information.

Step 3: Conclusion

Since the outcome is uncertain and depends on various factors, the most appropriate choice is that it is impossible to predict how the difference will change.

Final Answer

$\boxed{D}$

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