Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Analyze the data in the table below and determine whether the equation that produced the predicted values represents a good line of best fit.

| Enrollment | January | February | March | April | May | June |
|------------|---------|----------|-------|-------|-----|------|
| Actual | 12 | 14 | 14 | 13 | 16 | 14 |
| Predicted | 8 | 15 | 15 | 12 | 17 | 15 |
| Residual | 4 | -1 | -1 | 1 | -1 | -1 |

Options:
A. No, the equation is not a good fit because the sum of the residuals is a large number.
B. No, the equation is not a good fit because the residuals are all far from zero.
C. Yes, the equation is a good fit because the residuals are all far from zero.
D. Yes, the equation is a good fit because the sum of the residuals is a small number.

Sagot :

GinnyAnswer
To determine whether the equation that produced the predicted values represents a good line of best fit, we need to analyze several key components:

1. Sum of the Residuals:
- The residuals are calculated as the difference between the actual and predicted values for each month.
- Given residuals: [4, -1, -1, 1, -1, -1]
- Sum of the residuals: 4 + (-1) + (-1) + 1 + (-1) + (-1) = 1

2. Magnitude of Residuals:
- For a good fit, the residuals should not be excessively large in magnitude.
- Given residuals: [4, -1, -1, 1, -1, -1]
- Observing these residuals, we notice that 4 is significantly higher in magnitude compared to the others.

3. Good Fit Criteria:
- If the sum of the residuals is around zero, it indicates that the positive and negative errors balance each other out.
- Small residuals indicate a close prediction to the actual values, suggesting accuracy.

Conclusion:
- Sum of the Residuals: The sum of the residuals is 1, which is a small number. This suggests that overall the errors balance out well.
- Residual Magnitude: However, one of the residuals (4) is quite large in magnitude, deviating considerably from zero.

Given these observations:
- The small sum of the residuals indicates that the errors almost balance each other out.
- The statement "No, the equation is not a good fit because the sum of the residuals is a large number" is incorrect because the sum is actually small (1).
- The statement "No, the equation is not a good fit because the residuals are all far from zero" looks at the magnitude and the presence of a residual (4) far from zero could imply a poor fit.
- The statement "Yes, the equation is a good fit because the residuals are all far from zero" is incorrect because good residuals should be close to zero.
- The statement "Yes, the equation is a good fit because the sum of the residuals is a small number" correctly identifies the balance of residuals, despite one being large, the overall assessment is correct based on the given fit criteria.

Thus, the most appropriate conclusion is:

Yes, the equation is a good fit because the sum of the residuals is a small number.
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.