Use the data entry method in your scientific calculator to enter the following measurements.

(6, 11), (8, 7), and (7, 9).

Recall the proper memories to find the correlation coefficient, *r*.

*r* =

Recall the proper memories to find the *y*-intercept, *a*, of the line.

*a* =

Recall the proper memories to find the slope, *b*, of the line.

To calculate the **correlation coefficient (r)**, **y-intercept (a)**, and **slope (b)** of the line using the data points \((6, 11), (8, 7), (7, 9)\), we will follow these steps:

### 1. Entering Data into a Scientific Calculator:
You will need to enter the values of \( x \) and \( y \) into your calculator's **statistical mode**.

Here are the values:

\[
\begin{aligned}
x_1 &= 6, &y_1 &= 11 \\
x_2 &= 8, &y_2 &= 7 \\
x_3 &= 7, &y_3 &= 9 \\
\end{aligned}
\]

Once your calculator is set to regression mode (usually denoted as "Lin" or "LinReg" for linear regression), follow the steps to input these values:

- Input \( x = 6 \) and \( y = 11 \),
- Input \( x = 8 \) and \( y = 7 \),
- Input \( x = 7 \) and \( y = 9 \).

### 2. Finding the Correlation Coefficient (*r*):
After entering the data, use the regression function to calculate the **correlation coefficient (r)**. This measures the strength of the linear relationship between \( x \) and \( y \).

Using the formula \( r = \frac{n\sum xy - \sum x \sum y}{\sqrt{\left(n\sum x^2 - (\sum x)^2\right)\left(n\sum y^2 - (\sum y)^2\right)}} \), your calculator will provide you with:

\[
r = -1
\]

This means the data points have a perfect negative correlation.

### 3. Finding the y-Intercept (*a*):
Next, use the regression function to find the **y-intercept (a)**. It is calculated using the equation of the regression line \( y = a + bx \), where \( a \) is the y-intercept. Your calculator will give you:

\[
a = 25
\]

### 4. Finding the Slope (*b*):
Finally, the **slope (b)** of the line is found using the regression function, or calculated with the formula:

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

The calculator will yield:

\[
b = -2
\]

### Summary:
- **Correlation coefficient (r):** -1
- **y-intercept (a):** 25
- **Slope (b):** -2

Would you like more details on these calculations or how to input them into your specific calculator model?

### Follow-up Questions:
1. How does the correlation coefficient \( r \) relate to the strength of the linear relationship?
2. What does a slope of \( b = -2 \) imply about the relationship between \( x \) and \( y \)?
3. How is the y-intercept \( a = 25 \) interpreted in this context?
4. What happens when the correlation coefficient is 0?
5. Can you explain how you could use this line equation \( y = a + bx \) to predict values?

### Tip:
Always double-check that the calculator is in the correct mode for regression (LinReg) when solving for \( r \), \( a \), and \( b \).

Use the data entry method in your scientific calculator to enter the following measurements: (6, 11), (8, 7), and (7, 9). Recall the proper memories to find the correlation coefficient, *r*. *r* = Recall the proper memories to find the *y*-intercept, *a*, of the line. *a* = Recall the proper memories to find the slope, *b*, of the line.

Learn how to calculate the correlation coefficient, slope, and y-intercept using data points (6, 11), (8, 7), and (7, 9). This problem covers key statistical concepts such as linear regression and the Pearson correlation coefficient. Suitable for students in Grades 10-12.

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