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Find the correlation coefficient, r, of the data described below.
Playing video games makes Jackie so happy that she thinks it even helps her complete more schoolwork. Jackie's roommate Hunter is skeptical, so over the next few days, Hunter asks Jackie about her progress on her daily reading.
For each day, Hunter notes the number of minutes Jackie spends playing video games, x. He also takes the number of pages Jackie reads and divides it by the total number of pages assigned, y.
Minutes playing video games	Percentage of reading assignment
34	58
78	45
80	54
94	47
95	46
Round your answer to the nearest thousandth.
r=

To find the correlation coefficient \( r \) between two sets of data, we can use the following formula:

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

Where:
- \( x \) represents the independent variable (minutes playing video games),
- \( y \) represents the dependent variable (percentage of reading assignment completed),
- \( n \) is the number of data points.

Let's break down the problem into steps:

### Step 1: Calculate the necessary sums:
1. \( \sum x \) — Sum of the \( x \)-values (minutes playing video games)
2. \( \sum y \) — Sum of the \( y \)-values (percentage of reading completed)
3. \( \sum xy \) — Sum of the products of \( x \) and \( y \)
4. \( \sum x^2 \) — Sum of the squares of the \( x \)-values
5. \( \sum y^2 \) — Sum of the squares of the \( y \)-values

Here are the data points:

\[
x = [34, 78, 80, 94, 95]
\]
\[
y = [58, 45, 54, 47, 46]
\]

Now, let's calculate the correlation coefficient \( r \).It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like help walking through the calculations manually or have any other questions about the process?

Here are 5 related questions to expand your understanding:

1. How do changes in the data points affect the correlation coefficient?
2. What is the difference between positive and negative correlation?
3. How is a correlation coefficient interpreted in real-world examples?
4. What other methods can you use to measure relationships between two variables?
5. How do outliers influence the correlation coefficient?

**Tip:** A correlation coefficient close to 1 or -1 indicates a strong relationship, while values near 0 suggest little to no relationship.

Find the correlation coefficient, r, of the data described below.
Playing video games makes Jackie so happy that she thinks it even helps her complete more schoolwork. Jackie's roommate Hunter is skeptical, so over the next few days, Hunter asks Jackie about her progress on her daily reading. For each day, Hunter notes the number of minutes Jackie spends playing video games, x. He also takes the number of pages Jackie reads and divides it by the total number of pages assigned, y.
Minutes playing video games	Percentage of reading assignment
34	58
78	45
80	54
94	47
95	46
Round your answer to the nearest thousandth.

Learn how to calculate the correlation coefficient, r, between the time spent playing video games and the percentage of a reading assignment completed. Using statistical formulas, this example demonstrates a real-world application of the Pearson correlation coefficient. Suitable for students in Grades 10-12.

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