Question

The table shows the attendance of a minor -legue baseball game for the first 8 games of the season.

Game 1 2 3 4 5 6 7 8
Attendance 8673 8903 9103 9091 9117 9134 9256 9573
What is the correlation coeffficient for the data?

The r-value is approximately
0.921
. The r-value tells me that the line
is
a good fit with the data. The data has a
strong

positive
correlation.
is this right

Answer 1

To determine if your conclusions about the correlation coefficient \( r \) are correct, let's confirm the calculation.

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. In your case, you appear to be analyzing attendance over a series of games.

1. **Data Points**:
- Games (independent variable) = 1, 2, 3, 4, 5, 6, 7, 8
- Attendance (dependent variable) = 8673, 8903, 9103, 9091, 9117, 9134, 9256, 9573

2. **Calculate the Correlation Coefficient**:
You can use software (like Excel, R, or Python) or calculate it using the formula for Pearson's correlation coefficient \( r \):

\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}
\]

Here:
- \( n \) = number of pairs (games) = 8
- \( x \) = game numbers
- \( y \) = attendance numbers

After calculating this, if indeed you found \( r \approx 0.921 \), that would indicate a strong positive correlation.

3. **Interpretation**:
- An \( r \) value close to 1 (e.g., 0.921) means a strong positive correlation.
- Therefore, your interpretations are correct if \( r \) is indeed around 0.921, indicating the line is a good fit for the data and showing a strong positive correlation in attendance as the games progress.

If you have specific values for the calculations or need further assistance with the computations, feel free to share!