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.