https://file.aiquickdraw.com/mathbot/file/17265249969622keemijl.jpg

The image presents a table with two variables \( x \) and \( y \), and a multiple-choice question asking for the identification and correction of an error in determining the line of best fit.

Here is the data from the table:

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

The question asks to identify the mistake the student made in finding the equation of the line of best fit for this data. The options are:

**A:** The student switched the numbers in the equation. The line of best fit is \( y = 1.83 + 0.25x \).  
**B:** The student did not notice that the data set is too small for a linear regression to be useful.  
**C:** The student did not make it clear that the line of best fit is only an approximation of the data.  
**D:** The student switched the order of the data. The data for \( x \) should be entered in \( L_1 \), and the data for \( y \) should be entered in \( L_2 \).

### Analysis:

- The data points clearly show a pattern that could be modeled with linear regression, so option **B** is incorrect.
- The problem likely revolves around the proper handling or interpretation of the data in the linear regression process, possibly switching \( x \) and \( y \).
- The best-fit equation \( y = 1.83 + 0.25x \) provided in option **A** seems plausible for these data points when using the correct methodology.

Based on this, the correct answer is likely **D**, as switching the data entry order in lists \( L_1 \) and \( L_2 \) (commonly used in calculators) could lead to a mistake in calculating the regression.

Let me know if you would like to explore this further or get any details!

### Related Questions:

1. What is the method to calculate the slope in linear regression?
2. How do you determine the residuals when fitting a line of best fit?
3. Why is it important to input data correctly into a graphing calculator for linear regression?
4. What is the interpretation of the slope and intercept in the context of real data?
5. How can you check if a line of best fit is appropriate for a data set?

**Tip:** Always double-check how data is entered into statistical tools to avoid confusion with the 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.

Learn how to identify and correct errors in determining the equation for the line of best fit using linear regression. The problem involves analyzing data points to find the correct line of best fit equation, addressing common mistakes in input order and interpretation. Suitable for students in Grades 9-12.

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