Find the correlation coefficient between x and y and write down the equation of regression has from the following: n=25,Σx=125,Σxy=508,Σy=100,Σy²=460

To find the correlation coefficient (\( r \)) and the equation of the regression line, we can use the following formulas:

### 1. Correlation Coefficient (\( r \)):
The correlation coefficient \( r \) is given by:

\[
r = \frac{n \cdot \Sigma xy - \Sigma x \cdot \Sigma y}{\sqrt{\left( n \cdot \Sigma x^2 - (\Sigma x)^2 \right) \cdot \left( n \cdot \Sigma y^2 - (\Sigma y)^2 \right)}}
\]

However, since \( \Sigma x^2 \) is not provided, we can't directly calculate \( r \) from the given information. It seems there's some missing information. Usually, \( \Sigma x^2 \) is also provided along with the other values. 

### 2. Regression Equation (\( y = mx + c \)):
The regression line \( y \) on \( x \) can be represented as:

\[
y = mx + c
\]

Where:
- \( m \) is the slope given by:
\[
m = \frac{n \cdot \Sigma xy - \Sigma x \cdot \Sigma y}{n \cdot \Sigma x^2 - (\Sigma x)^2}
\]

- \( c \) is the y-intercept given by:
\[
c = \frac{\Sigma y - m \cdot \Sigma x}{n}
\]

Again, since \( \Sigma x^2 \) is missing, we can’t find the exact values of \( r \), \( m \), and \( c \). 

### Conclusion:
Without \( \Sigma x^2 \), the correlation coefficient and the regression equation cannot be fully determined. 

Would you like to provide more information or do you have any questions?

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Here are 5 related questions:
1. How can the correlation coefficient help in understanding the relationship between two variables?
2. What is the significance of the slope in a regression equation?
3. How does the y-intercept influence the position of the regression line?
4. What are some common applications of regression analysis in real-life situations?
5. How can you interpret the value of the correlation coefficient?

**Tip:** When solving statistical problems, always ensure you have all the necessary data points for accurate calculations.

Learn how to calculate the correlation coefficient and regression equation using provided statistical data. This problem involves finding statistical relationships between variables and applying regression analysis formulas.

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