Compute the equation of the regression line for a dataset that has the statistics given below. Round the values of a and b to two decimal places. x=9, Sx=1, y=267, Sy=93, r=0.95

To compute the equation of the regression line, we use the formula for the equation of a line:

\[
y = a + bx
\]

Where:
- \( b \) is the slope of the regression line, calculated as:

\[
b = r \times \frac{S_y}{S_x}
\]

- \( a \) is the y-intercept, calculated using:

\[
a = \bar{y} - b \times \bar{x}
\]

Given:
- \( \bar{x} = 9 \)
- \( S_x = 1 \)
- \( \bar{y} = 267 \)
- \( S_y = 93 \)
- \( r = 0.95 \)

### Step 1: Calculate the slope \( b \)

\[
b = 0.95 \times \frac{93}{1} = 0.95 \times 93 = 88.35
\]

### Step 2: Calculate the y-intercept \( a \)

\[
a = 267 - (88.35 \times 9) = 267 - 795.15 = -528.15
\]

### Final Answer:
The equation of the regression line is:

\[
y = -528.15 + 88.35x
\]

Let me know if you want more details or have any questions.

Here are five related questions to explore further:
1. How does the correlation coefficient \( r \) affect the slope of the regression line?
2. What would the regression equation be if the correlation \( r \) were negative?
3. How can we use the regression equation to make predictions?
4. What is the interpretation of the y-intercept in a regression line?
5. How do outliers affect the regression equation?

**Tip:** The correlation coefficient \( r \) tells you not only the strength of the relationship but also the direction (positive or negative) of the linear relationship between the variables.

Learn how to compute the linear regression equation for a dataset with given statistics: x̄=9, ȳ=267, Sx=1, Sy=93, and correlation coefficient r=0.95. This solution demonstrates how to calculate the slope and intercept, resulting in the regression equation y = -528.15 + 88.35x.

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