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To determine the least squares regression line and the correlation coefficient, we'll use the following formulas and given values.

### 1. Determine the Least Squares Regression Line

The least squares regression line has the form:
\[
\hat{y} = a + bx
\]
where:
- \( b = \frac{n \sum xy - \sum x \sum y}{n \sum x^2 - (\sum x)^2} \)
- \( a = \frac{\sum y - b \sum x}{n} \)

#### Given values:
- \( n = 30 \)
- \( \sum x = 294 \)
- \( \sum y = 361 \)
- \( \sum x^2 = 3834 \)
- \( \sum y^2 = 5175 \)
- \( \sum xy = 3258 \)

Let's calculate \( b \) first:

\[
b = \frac{30 \times 3258 - 294 \times 361}{30 \times 3834 - (294)^2}
\]

Then, calculate \( a \):

\[
a = \frac{361 - b \times 294}{30}
\]

### 2. Determine the Correlation Coefficient \( r \)

The formula for the correlation coefficient \( r \) is:
\[
r = \frac{n \sum xy - \sum x \sum y}{\sqrt{\left(n \sum x^2 - (\sum x)^2\right) \left(n \sum y^2 - (\sum y)^2\right)}}
\]

Using the values given, substitute into this formula to solve for \( r \).

Let me calculate these values.It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you'd like, I can guide you through the calculations manually. Let me know if you have any questions or if you'd like assistance with a specific part of the problem.

Here are some additional questions you may find helpful:
1. How is the slope \( b \) of a regression line interpreted in context?
2. What does the correlation coefficient \( r \) tell us about the strength of the relationship between \( x \) and \( y \)?
3. How can you determine if a regression line is a good fit for the data set?
4. What is the significance of the intercept \( a \) in a regression line?
5. How would the regression line change if additional data points were added to the data set?

**Tip:** When calculating by hand, always keep track of each step to minimize rounding errors.

The given quantities below were calculated from a sample data set. Determine the least squares regression line and the correlation coefficient. Round values to four decimal places if necessary.

Learn how to determine the least squares regression line and correlation coefficient using given sample data values. This problem covers regression analysis concepts and provides formulas for calculating slope, intercept, and correlation coefficient. Suitable for college-level statistics students.

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