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The question asks to "describe and correct the error a student made in determining the equation for the line of best fit for the data in the table."

Here is the data provided in the table:

| x  | y  |
|----|----|
| 3  | 4  |
| 6  | 17 |
| 9  | 28 |
| 12 | 40 |
| 15 | 55 |
| 18 | 67 |
| 21 | 72 |

The correct answer choices are:

- **A**: The student did not notice that the data set is too small for a linear regression to be useful.
- **B**: The student did not make it clear that the line of best fit is only an approximation of the data.
- **C**: The student switched the numbers in the equation. The line of best fit should be written as \( y = 0.25x + 1.83 \).
- **D**: The student switched the order of the data. The data for \(x\) should be entered in L1, and the data for \(y\) should be entered in L2. The line of best fit is \( y = 0.94x + 6.86 \).

Looking at the context, the error seems to be **option C**, where the student reversed the coefficients and the equation should be written as \( y = 0.25x + 1.83 \), not \( y = 1.83x + 0.25 \). The equation given in the right-hand side "Line of best fit \( y = 0.25x + 1.83 \)" confirms this correction.

Would you like more details or have any questions?

### Here are 5 related questions:
1. What is the importance of calculating a line of best fit in statistics?
2. How does linear regression help in making predictions from data?
3. Can you explain why the order of data entry in L1 and L2 affects the regression calculation?
4. How is the slope of the line \( 0.25 \) in \( y = 0.25x + 1.83 \) interpreted in real-life contexts?
5. What does the \( y \)-intercept \( 1.83 \) represent in the equation of the line of best fit?

### Tip: 
Always verify the order of variables when entering data for linear regression to avoid switching errors between dependent and independent variables.

Describe and correct the error a student made in determining the equation for the line of best fit for the data in the table. X-values: [3, 6, 9, 12, 15, 18, 21], Y-values: [4, 17, 28, 40, 55, 67, 72]

Learn how to identify and correct errors in determining the equation for the line of best fit using linear regression. The example includes X-values [3, 6, 9, 12, 15, 18, 21] and Y-values [4, 17, 28, 40, 55, 67, 72], with the correct equation being y = 0.25x + 1.83. Suitable for high school students.

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