The equation of the regression line expresses the relationship between two variables: home average attendance and runs scored.

The general form of a regression equation is:

$\hat{y} = b_0 + b_1 x$

Where:

• $\hat{y}$ is the predicted value of the dependent variable (in this case, attendance),
• $x$ is the independent variable (in this case, runs),
• $b_0$ is the y-intercept (the predicted attendance when runs = 0), and
• $b_1$ is the slope (the change in attendance for each additional run scored).

From the problem, it appears we are trying to find how attendance depends on runs. Based on this, the regression line would have the form:

$\hat{\text{Attendance}} = b_0 + b_1 \cdot \text{Runs}$

You are asked to choose between two options and to round the coefficients to the nearest integer.

Option A:

$\hat{\text{Attendance}} = 25000 + 1200 \cdot \text{Runs}$

This indicates that for every additional run scored, the attendance increases by approximately 1200 people, and when no runs are scored, the predicted attendance would be around 25,000 people.

Option B:

This seems incorrect because it reverses the dependent and independent variables, implying that runs depend on attendance. Therefore, Option A is the correct regression equation.

Thus, the equation of the regression line is:

$\hat{\text{Attendance}} = 25000 + 1200 \cdot \text{Runs}$

Let me know if you have any questions or want details on this.

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Here are 5 related questions you might want to explore:

1. How does the standard error of the regression line affect predictions?
2. What does the slope of the regression line suggest about the relationship between runs and attendance?
3. What is the R-squared value for this regression, and what does it indicate?
4. Can we predict attendance accurately if we only know the runs scored?
5. How do other factors (such as team popularity) affect attendance beyond runs scored?

Tip: Always verify the assumptions of regression analysis, such as linearity and independence of errors, to ensure that your model is appropriate for the data.