To determine the equation of the regression line $\hat{y} = b_1x + b_0$, we need to calculate the slope $b_1$ and intercept $b_0$ using the given data.

Step 1: Calculate the slope ($b_1$)

The formula for $b_1$ is: $b_1 = \frac{SS_{xy}}{SS_{xx}}$ Substitute the given values: $b_1 = \frac{-49.75}{1843.87} \approx -0.027$

Step 2: Calculate the intercept ($b_0$)

The formula for $b_0$ is: $b_0 = \bar{y} - b_1\bar{x}$ To find $\bar{x}$ and $\bar{y}$: $\bar{x} = \frac{\Sigma X}{n} = \frac{475}{8} = 59.375$ $\bar{y} = \frac{\Sigma Y}{n} = \frac{60}{8} = 7.5$

Now substitute into the formula for $b_0$: $b_0 = 7.5 - (-0.027)(59.375)$ $b_0 \approx 7.5 + 1.603125 \approx 9.1$

Step 3: Write the equation

The regression equation is: $\hat{y} = -0.027x + 9.1$

Final Answer:

The correct choice is: $\text{y-hat = -0.027x + 9.1}$

Would you like a detailed explanation of any of the steps? Here are some related questions you might find helpful:

1. How do you interpret the slope and intercept in this context?
2. What are some real-world applications of regression equations?
3. How do residuals relate to the regression line?
4. How can the coefficient of determination ($R^2$) be calculated and interpreted?
5. What assumptions are made in a simple linear regression model?

Tip: Always check for units and the context of your variables to make meaningful interpretations of the regression equation!