Σx=162
Σy=675
ΣX2=2652
ΣY2=46459
ΣXY=10967
N=10

calculate correlation 

To calculate the correlation coefficient \( r \) using the given data, we use the formula:

\[
r = \frac{N \sum XY - \sum X \sum Y}{\sqrt{(N \sum X^2 - (\sum X)^2)(N \sum Y^2 - (\sum Y)^2)}}
\]

Given:
\[
\sum X = 162, \quad \sum Y = 675, \quad \sum X^2 = 2652, \quad \sum Y^2 = 46459, \quad \sum XY = 10967, \quad N = 10
\]

Let's calculate it step by step.

### Step 1: Calculate the numerator
\[
N \sum XY - \sum X \sum Y = 10 \times 10967 - 162 \times 675
\]

### Step 2: Calculate the denominator
\[
\sqrt{(N \sum X^2 - (\sum X)^2)(N \sum Y^2 - (\sum Y)^2)} 
= \sqrt{(10 \times 2652 - 162^2) \times (10 \times 46459 - 675^2)}
\]

### Step 3: Compute the correlation coefficient \( r \).

I'll calculate it now.The correlation coefficient \( r \) is approximately **0.203**.

Would you like more details, or do you have any questions? 

Here are five related questions to expand your understanding:
1. How does the value of \( r \) indicate the strength of the correlation?
2. What does a correlation coefficient close to 0 imply about the relationship between the variables?
3. How would the calculation differ if the sample size \( N \) increased?
4. Can the correlation coefficient \( r \) be negative? If so, what would that indicate?
5. How can you calculate the coefficient of determination (\( r^2 \)) from the correlation coefficient?

**Tip:** The correlation coefficient only measures the strength of a linear relationship. For non-linear relationships, other statistical methods might be more appropriate.

Learn how to calculate the correlation coefficient (r) using the given data Σx=162, Σy=675, ΣX2=2652, ΣY2=46459, ΣXY=10967. Follow a step-by-step explanation of the formula and computation process. Suitable for undergraduate level study.

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