The question asks us to determine the line of best fit for the given data based on the linear regression calculation. Here's the step-by-step explanation:

Given Information:

The equation for the line of best fit is: $y = ax + b$

• $a = -3.1$ (slope)
• $b = 12.9$ (y-intercept)

The line of best fit:

Substituting the values of $a$ and $b$ into the equation: $y = -3.1x + 12.9$

Correct Answer:

From the options provided, the correct answer is B: $y = -3.1x + 12.9$.

Let me know if you'd like additional clarification or details! 😊

Related Questions:

1. What does the slope ($a = -3.1$) indicate about the relationship between $x$ and $y$ in this regression?
2. How can the correlation coefficient ($r$) help evaluate the fit of the line to the data?
3. What does the $b = 12.9$ (y-intercept) signify in this context?
4. If you had to predict $y$ for $x = 6$, what value would you get using this regression line?
5. How does a negative slope affect the interpretation of this data?

Tip:

When interpreting regression equations, always check the context and signs of $a$ (slope) and $b$ (intercept) to ensure the equation aligns with the data's behavior!