To solve this, we will use simple linear regression, which fits a line to the data to predict $Y$ based on $X$. The equation of a regression line is:

$Y = a + bX$

Where:

• $a$ is the intercept
• $b$ is the slope
• The correlation coefficient (r) measures the strength and direction of the linear relationship.

The slope $b$ is calculated as:

$b = \frac{n(\sum XY) - (\sum X)(\sum Y)}{n(\sum X^2) - (\sum X)^2}$

The intercept $a$ is calculated as:

$a = \frac{\sum Y - b(\sum X)}{n}$

Where $n$ is the number of data points.

The correlation coefficient $r$ is calculated as:

[ r = \frac{n(\sum XY) - (\sum X)(\sum Y)}{\sqrt{[n(\sum X^2) - (\sum X)^2][n(\sum Y^2) - (\sum Y)^2]}} ]

I'll calculate the values now.1) The slope of the regression line predicting $Y$ from $X$ is $-1.38$.

2. The intercept of the regression line is $271.81$.

3. The correlation between $X$ and $Y$ is $-0.89$, indicating a strong negative linear relationship.

Would you like any further details on the calculations or the interpretation?

Here are 5 follow-up questions to extend understanding:

1. What does the slope of $-1.38$ indicate about the relationship between $X$ and $Y$?
2. How can we interpret the negative correlation of $-0.89$?
3. What would happen to the line if the intercept were higher or lower?
4. Can we predict $Y$ if $X$ is outside the provided range?
5. What is the meaning of the residuals in a regression line?

Tip: A negative slope in regression implies that as the predictor variable increases, the response variable decreases.